diff --git a/bindings/Mandos/python/Deformable3D.cpp b/bindings/Mandos/python/Deformable3D.cpp
index 820086fbdf5675dfaae762896e9466a68288f469..24529bb1d2ac2b3fd72fafba4195a5c667f894bc 100644
--- a/bindings/Mandos/python/Deformable3D.cpp
+++ b/bindings/Mandos/python/Deformable3D.cpp
@@ -15,6 +15,7 @@
 #include <nanobind/stl/string.h>
 #include <nanobind/stl/vector.h>
 
+
 NB_MAKE_OPAQUE(mandos::core::DiffParameterHandleV)
 
 void mandos::py::wrapDeformable3D(nb::module_ &m)
@@ -84,9 +85,31 @@ void mandos::py::wrapDeformable3D(nb::module_ &m)
              nb::arg("x") = true,
              nb::arg("y") = true,
              nb::arg("z") = true)
-        .def("fixed_dof_vector", &Deformable3D::getFixedDofVector);
+        .def("fixed_dof_vector", &Deformable3D::getFixedDofVector)
+    // Differential parameters
+    //--------------------------
+    // Mass Spring
+    .def("diff", [](const Deformable3D &self, mandos::core::MassSpring::Parameters parameter) {
+        switch (parameter) {
+            case mandos::core::MassSpring::Stiffness: {
+                mandos::core::DiffParameterHandle<mandos::core::Particle3DTag,
+                                                  mandos::core::MassSpring,
+                                                  mandos::core::MassSpring::Stiffness>
+                    paramHandle(self.handle());
+                return mandos::core::DiffParameterHandleV(paramHandle);
+            }
+            case mandos::core::MassSpring::RestLength: {
+                mandos::core::DiffParameterHandle<mandos::core::Particle3DTag,
+                                                  mandos::core::MassSpring,
+                                                  mandos::core::MassSpring::RestLength>
+                    paramHandle(self.handle());
+                return mandos::core::DiffParameterHandleV(paramHandle);
+            }
+        }
+    });
 }
 
+
 mandos::core::SimulationObject<mandos::core::Particle3DTag> &mandos::py::Deformable3D::simObject()
 {
     return m_handle.simulationObject();
diff --git a/bindings/Mandos/python/Differentiable.cpp b/bindings/Mandos/python/Differentiable.cpp
index 184e88de44ec5340acda6565e409a77a54cf85c2..10106242a8c2ff93b508a3117f2ce46e55e869ff 100644
--- a/bindings/Mandos/python/Differentiable.cpp
+++ b/bindings/Mandos/python/Differentiable.cpp
@@ -4,7 +4,7 @@
 #include <Mandos/Core/Differentiable.hpp>
 
 #include <nanobind/eigen/dense.h>
-
+#include <nanobind/stl/vector.h>
 namespace nb = nanobind;
 
 NB_MAKE_OPAQUE(mandos::core::DiffParameterHandleV)
diff --git a/bindings/Mandos/python/Energies/CosseratBendingRod.cpp b/bindings/Mandos/python/Energies/CosseratBendingRod.cpp
index 21fbd3e75e5d5da97b42a69d389c21e42b032071..5b946e17dac84af6f165595e47adefeeaebab2e9 100644
--- a/bindings/Mandos/python/Energies/CosseratBendingRod.cpp
+++ b/bindings/Mandos/python/Energies/CosseratBendingRod.cpp
@@ -6,6 +6,7 @@
 
 #include <nanobind/eigen/dense.h>
 #include <nanobind/stl/array.h>
+#include<Mandos/python/RigidBody.hpp>
 
 void mandos::py::energies::wrapCosseratBendingRod(nb::module_ &m)
 {
@@ -40,14 +41,21 @@ void mandos::py::energies::wrapCosseratBendingRod(nb::module_ &m)
              [](const mandos::core::CosseratBendingRod &massSpring, int elementId) {
                  return massSpring.getParameterSet(elementId);
              })
+
         .def("set_parameter_set",
              [](mandos::core::CosseratBendingRod &massSpring,
                 int elementId,
                 const mandos::core::CosseratBendingRod::ParameterSet &parameterSet) {
                  massSpring.setParameterSet(elementId, parameterSet);
+             })
+        
+        .def("compute_bending_energy",
+             [](const mandos::core::CosseratBendingRod &bendingRod, const mandos::py::RigidBodyCloud3D &rbCloud) {
+                 return bendingRod.computeEnergy(rbCloud.simObject().mstate);
              });
 
     nb::enum_<mandos::core::CosseratBendingRod::Parameters>(cosseratBendingRod, "Parameters")
         .value("intrinsic_darboux", mandos::core::CosseratBendingRod::IntrinsicDarboux)
+        .value("stiffness_tensor", mandos::core::CosseratBendingRod::StiffnessTensor)
         .export_values();
 }
diff --git a/bindings/Mandos/python/Energies/CosseratRodAlignment.cpp b/bindings/Mandos/python/Energies/CosseratRodAlignment.cpp
index f17544270383d819c1f2b425ce36022e2e30dc12..da5733c6520666c44bad7c69a457647e47bd6f3e 100644
--- a/bindings/Mandos/python/Energies/CosseratRodAlignment.cpp
+++ b/bindings/Mandos/python/Energies/CosseratRodAlignment.cpp
@@ -6,6 +6,7 @@
 
 #include <nanobind/eigen/dense.h>
 #include <nanobind/stl/array.h>
+#include<Mandos/python/RigidBody.hpp>
 
 void mandos::py::energies::wrapCosseratRodAlignment(nb::module_ &m)
 {
@@ -42,5 +43,10 @@ void mandos::py::energies::wrapCosseratRodAlignment(nb::module_ &m)
                 int elementId,
                 const mandos::core::CosseratRodAlignment::ParameterSet &parameterSet) {
                  massSpring.setParameterSet(elementId, parameterSet);
+             })
+        
+        .def("compute_cosserat_energy",
+             [](const mandos::core::CosseratRodAlignment &cosseratRod, const mandos::py::RigidBodyCloud3D &rbCloud) {
+                 return cosseratRod.computeEnergy(rbCloud.simObject().mstate);
              });
 }
diff --git a/bindings/Mandos/python/Model.cpp b/bindings/Mandos/python/Model.cpp
index 224d252cc7d0b762b4eb07e59106629cac413489..573815930976282be15580658797fe6ccd049c64 100644
--- a/bindings/Mandos/python/Model.cpp
+++ b/bindings/Mandos/python/Model.cpp
@@ -27,7 +27,7 @@
 #include <optional>
 
 #include <fmt/format.h>
-
+#include <Mandos/Core/SystemMatrix.hpp>
 void mandos::py::wrapModel(nb::module_ &m)
 {
     const nb::class_<core::Model> model_(m, "Model_");
@@ -273,6 +273,17 @@ void mandos::py::wrapModel(nb::module_ &m)
 
                  model.computeEnergyAndGradient(h, g);
              })
+        .def("compute_hessian",
+             [](Model &model, const mandos::core::Scalar h) {
+                 auto nDof = model.nDof();
+                 mandos::core::Vec g(nDof);
+                 g.setZero();
+                 mandos::core::SystemMatrix hessian(nDof, nDof);
+                 // We need to compute advection to ensure inertial forces are correct
+                 model.computeAdvection(h);
+
+                 model.computeEnergyGradientAndHessian(h, g, hessian);
+             })
         .def("detect_collisions",
              [](Model &model) {
                  // Ensure all the graph is updated
diff --git a/bindings/Mandos/python/RigidBody.cpp b/bindings/Mandos/python/RigidBody.cpp
index 25258bdacc65da3fd5a7d965466f28f78f623f0f..c94e2afdf25f35fbb864973d5e3b557c8c133b9b 100644
--- a/bindings/Mandos/python/RigidBody.cpp
+++ b/bindings/Mandos/python/RigidBody.cpp
@@ -75,7 +75,19 @@ void wrapRigidBody(nb::module_ &m)
             transform.block<3, 1>(0, 3) = self.x().segment<3>(0);                                // Position
             transform(3, 3) = 1.0;
             return transform;
-        });
+        })
+
+        .def("diff", [](RigidBody3D<core::RigidBodyTag> &self, core::MassSpring::Parameters parameter) {
+        switch (parameter) {
+                case core::MassSpring::Stiffness: {
+                mandos::core::DiffParameterHandle<mandos::core::RigidBodyTag,
+                                                      mandos::core::MassSpring,
+                                                      mandos::core::MassSpring::Stiffness>
+                    paramHandle(self.handle());
+                return mandos::core::DiffParameterHandleV(paramHandle);
+            }
+        }
+    });
 
     nb::class_<RigidBody3D<core::RigidBodyGlobalTag>>(m, "RigidBodyGlobal3D")
         .def_prop_rw("x", &RigidBody3D<core::RigidBodyGlobalTag>::x, &RigidBody3D<core::RigidBodyGlobalTag>::setX)
@@ -109,6 +121,7 @@ void wrapRigidBody(nb::module_ &m)
         .def_prop_rw("v", &RigidBodyCloud3D::v, &RigidBodyCloud3D::setV)
         .def_prop_ro("grad", &RigidBodyCloud3D::grad)
         .def_prop_ro("hessian", &RigidBodyCloud3D::hessian)
+        .def_prop_ro("hessian_dense", &RigidBodyCloud3D::hessianDense, nb::rv_policy::copy)
         .def_prop_rw("mass", &RigidBodyCloud3D::mass, &RigidBodyCloud3D::setMass)
         .def_prop_rw("inertiaTensor", &RigidBodyCloud3D::inertiaTensor, &RigidBodyCloud3D::setInertiaTensor)
         .def("enable_gravity",
@@ -135,7 +148,29 @@ void wrapRigidBody(nb::module_ &m)
              nb::arg("z") = true)
         .def("fix_rotation", &RigidBodyCloud3D::fixRigidBodyRotation, nb::arg("index"))
         .def("clear_fixing", &RigidBodyCloud3D::clearFixing)
-        .def("fixed_dof_vector", &RigidBodyCloud3D::getFixedDofVector);
+        .def("fixed_dof_vector", &RigidBodyCloud3D::getFixedDofVector)
+    .def("diff", [](RigidBodyCloud3D &self, core::MassSpring::Parameters parameter) {
+        switch (parameter) {
+            case core::MassSpring::Stiffness: {
+                mandos::core::DiffParameterHandle<mandos::core::RigidBodyTag,
+                                                  mandos::core::MassSpring,
+                                                  mandos::core::MassSpring::Stiffness>
+                    paramHandle(self.handle());
+                return mandos::core::DiffParameterHandleV(paramHandle);
+            }
+        }
+    })
+    .def("diff", [](RigidBodyCloud3D &self, core::CosseratBendingRod::Parameters parameter) {
+        switch (parameter) {
+                case core::CosseratBendingRod::StiffnessTensor: {
+                mandos::core::DiffParameterHandle<mandos::core::RigidBodyTag,
+                                                      mandos::core::CosseratBendingRod,
+                                                      mandos::core::CosseratBendingRod::StiffnessTensor>
+                    paramHandle(self.handle());
+                return mandos::core::DiffParameterHandleV(paramHandle);
+            }
+        }
+    });
 }
 
 template <typename Tag>
@@ -292,6 +327,13 @@ const mandos::core::SparseMat &RigidBodyCloud3D::hessian() const
     return simObject().mstate.m_hessian;
 }
 
+const Eigen::MatrixXd RigidBodyCloud3D::hessianDense() const
+{
+    mandos::core::SparseMat sparseHessian = simObject().mstate.m_hessian;
+    Eigen::MatrixXd denseHessian = sparseHessian.toDense();
+    return denseHessian;
+}
+
 mandos::core::MassSpring &RigidBodyCloud3D::massSpring()
 {
     return simObject().template potential<mandos::core::MassSpring>();
diff --git a/bindings/Mandos/python/RigidBody.hpp b/bindings/Mandos/python/RigidBody.hpp
index 4c55d9b4021fde4970d14896936d3dc4f34be842..dc45b232b139fe9ec2c20862307bf2c428c30966 100644
--- a/bindings/Mandos/python/RigidBody.hpp
+++ b/bindings/Mandos/python/RigidBody.hpp
@@ -2,7 +2,7 @@
 #define MANDOS_PY_RIGIDBODY_HPP
 
 #include <nanobind/nanobind.h>
-
+#include <nanobind/eigen/dense.h>
 #include <Mandos/Core/Energies/GravityEnergy.hpp>
 #include <Mandos/Core/MechanicalStates/RigidBody.hpp>
 #include <Mandos/Core/MechanicalStates/RigidBodyGlobal.hpp>
@@ -85,6 +85,8 @@ struct RigidBodyCloud3D {
 
     const mandos::core::SparseMat &hessian() const;
 
+    const Eigen::MatrixXd hessianDense() const;
+
     mandos::core::MassSpring &massSpring();
     mandos::core::CosseratBendingRod &cosseratBendingRod();
     mandos::core::CosseratRodAlignment &cosseratRodAlignment();
diff --git a/examples/python/ColonExperiments/axis.obj b/examples/python/ColonExperiments/axis.obj
new file mode 100644
index 0000000000000000000000000000000000000000..e000459b8d1925a2caf4aa4b6aa368418b55348c
--- /dev/null
+++ b/examples/python/ColonExperiments/axis.obj
@@ -0,0 +1,2295 @@
+# Blender 4.1.1
+# www.blender.org
+o Sphere
+v 0.000000 0.083147 -0.055557
+v 0.000000 0.055557 -0.083147
+v 0.000000 0.019509 -0.098079
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+v 0.027060 0.070711 0.065328
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diff --git a/examples/python/ColonExperiments/colon.stl b/examples/python/ColonExperiments/colon.stl
new file mode 100644
index 0000000000000000000000000000000000000000..14cc1b95aba175de59d44167cd2b4d3ec8913809
Binary files /dev/null and b/examples/python/ColonExperiments/colon.stl differ
diff --git a/examples/python/ColonExperiments/demoJuanjoRigidColonAsDeformble.py b/examples/python/ColonExperiments/demoJuanjoRigidColonAsDeformble.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f19ce3af7f42b2a7b1e71d599779d959dac7855
--- /dev/null
+++ b/examples/python/ColonExperiments/demoJuanjoRigidColonAsDeformble.py
@@ -0,0 +1,307 @@
+import sys
+import numpy as np
+import meshio
+import polyscope as ps
+
+import os
+import pymandos
+
+from parallel_transport import compute_rotations_parallel_transport
+import polyscope.imgui as psim
+
+
+division_Coef = 1000 ### divie by 1000 to make the mm of the colon in meters
+endoscopeR = 0.5 * 11.5 / division_Coef#mm   radius of endoscope
+
+tubeL = 1500 / division_Coef 
+passiveBendingL = 45 / division_Coef #m
+activeBendingL = 110 /division_Coef # m 
+tipL = 20 / division_Coef ##m
+
+
+density_tube = 1700 
+density_passiveBending = 800
+density_activeBending = 600
+density_tip = 1000
+
+
+tubePoints = 100
+passiveBendingPoints = 4  #5
+activeBendingPoints = 10
+tipPoints = 3
+
+delta_xTube = tubeL / tubePoints
+delta_xPassiveBending = passiveBendingL / passiveBendingPoints
+delta_xActiveBending = activeBendingL / activeBendingPoints
+delta_xTip = tipL / tipPoints
+
+total_length = tipL + activeBendingL + passiveBendingL + tubeL
+n_points = tipPoints + activeBendingPoints + passiveBendingPoints + tubePoints 
+
+massVector = (
+    tubePoints * [density_tube   * np.pi * endoscopeR**2 * tubeL   / tubePoints] +
+    passiveBendingPoints * [density_passiveBending * np.pi * endoscopeR**2 * passiveBendingL / passiveBendingPoints] +
+    activeBendingPoints  * [density_activeBending  * np.pi * endoscopeR**2 * activeBendingL  / activeBendingPoints] +
+    tipPoints            * [density_tip           * np.pi * endoscopeR**2 * tipL            / tipPoints]
+)
+
+delta_x = total_length / n_points
+insertion_speed = 100 /division_Coef
+vUnit = np.zeros(3)
+m_point = []
+nNodes = 0
+playing = False
+
+def compute_edges(triangles):
+    # For each triangle, create its three edges
+    edges = np.vstack([
+        triangles[:, [0, 1]],
+        triangles[:, [1, 2]],
+        triangles[:, [2, 0]]
+    ])
+    # Sort each edge so that the order is consistent (smallest index first)
+    edges = np.sort(edges, axis=1)
+    # Remove duplicate edges
+    unique_edges = np.unique(edges, axis=0)
+    return unique_edges
+
+def create_model():
+    
+    ## load the colon
+    mesh = meshio.read("colon.stl")
+    triangles = mesh.cells_dict["triangle"]
+    edges = compute_edges(triangles)
+    x = mesh.points /division_Coef
+    
+    # ##  find the coordinates to place the endoscope
+    minZ = np.min(x[:,2])
+    
+    initalIndices = np.where (x[:,2]< minZ + 5 /division_Coef)
+    average = np.average(x[initalIndices], axis=(0))
+    print(average)
+    middlePoint = np.zeros((1,3))
+    middlePoint[0,0] = average[0]
+    middlePoint[0,1] = average[1]
+    middlePoint[0,2] = average[2]
+    m_point.extend(middlePoint)
+
+    print(average)
+
+    # ## find a vector, perpendicular to the colons' whole
+    p = x[initalIndices[0][0]]; q = x[initalIndices[0][1]]; r = x[initalIndices[0][2]]
+    pq = q-p
+    pr = r-p
+    v = np.cross(pq,pr)
+    global vUnit 
+    vUnit = v / (v**2).sum()**0.5   ##### carefull with the sign, if the endoscope goes to the wrong direction,change the sign!
+
+    # ### Creat the pymandos model
+    model = pymandos.Model()
+    # ## create the rod model
+    endoscope = model.add_rigidbody_cloud(name="endoscope")
+    
+    # Set initial conditions
+    positions = np.zeros((n_points, 6))
+    velocities = np.zeros((n_points, 6))
+
+    startingPos= np.array([middlePoint[0,0], middlePoint[0,1], middlePoint[0,2]])
+    for i, position in enumerate(positions):
+        if i<tipPoints:
+            delta_xLocal = delta_xTip
+        elif i< tipPoints + activeBendingPoints:
+            delta_xLocal = delta_xActiveBending
+        elif i<tipPoints + activeBendingPoints + passiveBendingPoints:
+            delta_xLocal = delta_xPassiveBending
+        else:
+            delta_xLocal = delta_xTube
+        if i==0:
+            position[0] = startingPos[0] 
+            position[1] = startingPos[1] 
+            position[2] = startingPos[2] 
+        else:
+            position[0] = startingPos[0] - delta_xLocal * vUnit[0]
+            position[1] = startingPos[1] - delta_xLocal * vUnit[1]
+            position[2] = startingPos[2] - delta_xLocal * vUnit[2]
+    
+        startingPos[0] = position[0]
+        startingPos[1] = position[1]
+        startingPos[2] = position[2]
+
+    positions = np.flip(positions,0) 
+    lin_pos = np.array([pos[:3] for pos in positions])
+    rotvecs = compute_rotations_parallel_transport(lin_pos)
+    for rotvec, pos in zip(rotvecs, positions):
+        pos[3:] = rotvec
+    endoscope.size = n_points
+    endoscope.x = positions
+    endoscope.v = velocities
+    # # Set up rigid body mass and inertia
+    endoscope.mass = massVector
+    endoscope.inertiaTensor = [massVector[_] *np.diag([1.0, 1.0, 1.0]) for _ in range(n_points)]
+    endoscope.disable_gravity()
+
+     # Rod energy
+    # A Rod is made of three diferent energies
+    # - MassSpring energy, which tries to keep distance between frames at a particular rest length 
+    # - CosseratBendingRod energy, which tries to keep frames aligned along the Z direction
+    # - CosseratRodAlignment energy, 
+    collision_stiffness = 3000
+    Ks_coef = 3000
+    stiffness_tensor_coef = 0.01693
+    cosserat_stiffness_coef = 1e3# * stiffness_tensor_coef
+
+    Ks = [Ks_coef for _ in range(n_points - 1)]
+    stiffness_tensor = [stiffness_tensor_coef * np.array([1,1,20]) for _ in range(n_points - 2)]
+    cosserat_stiffness = [cosserat_stiffness_coef for _ in range(n_points - 1)]
+
+    ## 21, 9, 6
+    for i in range(tubePoints -1, tubePoints + passiveBendingPoints):
+        stiffness_tensor[i]=  (0.00424/0.01693) *stiffness_tensor[i]  #9/21 *
+        # cosserat_stiffness[i]= 0.2 * cosserat_stiffness[i]
+        
+    for i in range(tubePoints + passiveBendingPoints, tubePoints + passiveBendingPoints + activeBendingPoints):
+        stiffness_tensor[i]= (0.00314/0.01693) * stiffness_tensor[i]
+        # cosserat_stiffness[i]= 0.15 * cosserat_stiffness[i]
+
+    for i in range(tubePoints + passiveBendingPoints + activeBendingPoints, n_points - 2):
+        stiffness_tensor[i]= 10 * stiffness_tensor[i]
+        # cosserat_stiffness[i]= 10 * cosserat_stiffness[i]
+    # cosserat_stiffness[n_points-2]= 10 * cosserat_stiffness[n_points-2]  #### this because the stiffnes tensor has 1 less element
+    
+    mass_spring = endoscope.mass_spring
+    cosserat_rod = endoscope.cosserat_rod_alignment
+    for i in range(n_points-1):
+        mass_spring.add_element([i, i+1], pymandos.energies.MassSpring.ParameterSet(x0 = endoscope.x[[i, i+1], 0:3], stiffness = Ks_coef))
+        cosserat_rod.add_element([i, i+1], pymandos.energies.CosseratRodAlignment.ParameterSet(x0 = endoscope.x[[i, i+1], :], cosserat_stiffness= cosserat_stiffness[i]))
+
+    bending_rod = endoscope.cosserat_bending_rod
+    for i in range(n_points-2):
+        bending_rod.add_element([i, i+1], pymandos.energies.CosseratBendingRod.ParameterSet(x0 = endoscope.x[[i, i+1], :], stiffness_tensor=stiffness_tensor[i]))
+
+    # ########### Map particles to rigid bodies for contact ####
+    mapping = model.add_rigidbody_point_mapping(endoscope, to_name="Collider")
+	## set the collision thresholds according to the endoscope diameter ##
+    collision_detection_threshold = 0.009
+    collision_threshold = 0.00575
+    indices = np.zeros((n_points - 1, 2), dtype=int)
+    for i in range(n_points):
+        mapping.add_particle(0 * np.array([1,0,0]), i)
+        if (i < (n_points - 1)):
+            indices[i, :] = np.array([i, i + 1])
+        # mapping.add_particle(collision_radius * np.array([1,0,0]), i)
+        # mapping.add_particle(collision_radius * np.array([-1,0,0]), i)
+        # mapping.add_particle(collision_radius * np.array([0,1,0]), i)
+        # mapping.add_particle(collision_radius * np.array([0,-1,0]), i)
+        # mapping.add_particle(collision_radius * np.array([0,0,1]), i)
+        # mapping.add_particle(collision_radius * np.array([0,0,-1]), i)
+    deformable = mapping.deformable   
+    ps.register_point_cloud("ColliderSC", deformable.x, radius=0.0)
+
+    
+
+#####  Prepare the rigid Colon  #############
+
+    colon_mesh = pymandos.SurfaceMesh()
+    colon_mesh.x = mesh.points /division_Coef
+    colon_mesh.indices = mesh.cells_dict["triangle"]
+    triangles = mesh.cells_dict["triangle"]
+    edgesColon = compute_edges(triangles)
+    global nNodes
+    nNodes = colon_mesh.x.shape[0]
+    
+    deformableColon = model.add_deformable_3d()
+    deformableColon.size =  nNodes            
+    nodesCoord = np.zeros(( nNodes , 3))
+    nodesCoord = colon_mesh.x
+    deformableColon.x = nodesCoord
+    deformableColon.v = np.zeros(( nNodes, 3))
+    massColon =  0.01 * np.ones( nNodes)
+    deformableColon.particle_mass = massColon
+       
+    for i in range(nNodes):
+        deformableColon.fix_particle(i)
+    deformableColon.disable_gravity()
+
+    rod_collider = deformable.add_collision_mesh(edges=indices.tolist(), dhat=collision_detection_threshold)
+    colon_collider = deformableColon.add_collision_mesh(edges=edgesColon.tolist(),triangles=colon_mesh.indices.tolist(), dhat=collision_detection_threshold)
+    print("Add collision pair")
+    collisionDeformable = model.add_collision_pair(colon_collider, rod_collider, stiffness = collision_stiffness, threshold = collision_threshold)
+    print("Collision pair added")
+    print("collisionDeformable.x =  ", collisionDeformable.x)
+
+    model.commit()
+    
+    # Render
+    axis_mesh = meshio.read("axis.obj")
+    scale_axis= 10 /division_Coef
+
+    # Render Endoscope
+    positions = np.array([x[:3] for x in endoscope.x])
+    for i in range(n_points):
+        endoscope_view = ps.register_surface_mesh(f"Endoscope_{i}", scale_axis * axis_mesh.points, axis_mesh.cells_dict["triangle"], 
+                                                  transparency=None)
+        endoscope_view.add_color_quantity("xyz", scale_axis * axis_mesh.points, enabled=True)
+    indices = np.array([(i, i+1) for i in range(n_points -1)])
+    endoscope_view = ps.register_curve_network("Endoscope", positions, indices, radius = 0.004, transparency=0.5)
+    ps.register_surface_mesh("Colon", mesh.points / division_Coef , mesh.cells_dict["triangle"], transparency=0.3)
+
+    ps.register_point_cloud("ColonFixedPoints",  deformableColon.x[nNodes :], radius=0.001,  transparency=0.3)
+    return model, deformableColon, collisionDeformable
+
+def simulate_callback(model, deformableColon, collisionDeformable):
+
+    step_parameters = pymandos.StepParameters()
+    step_parameters.h = 0.005
+    step_parameters.newton_iterations = 1500
+    step_parameters.cg_iterations = 250
+    step_parameters.cg_error = 1e-8
+    step_parameters.grad_norm = 1e-4
+    step_parameters.line_search_iterations = 10
+    step_parameters.accept_failed_solution = True
+    global playing
+    # if playing:
+    #     if psim.Button("Pause"):
+    #         playing = False
+    # elif psim.Button("Simulate"):
+    #     playing=True
+    playing=True
+    doStep = playing
+    if psim.Button("Step"):
+        doStep = True
+    endoscope = model.get_rigidbody_cloud("endoscope")
+
+    if doStep:
+        print(pymandos.step(model, step_parameters))
+        dx = np.array([0, 0, step_parameters.h * insertion_speed])
+        pos = endoscope.x.copy()
+        A = np.abs(np.asarray(pos[:, 0:3]) - np.asarray(m_point[0]))
+        index = (A ** 2).sum(1).argmin() -1
+
+        pos = np.array([x for x in endoscope.x])
+        endoscope.clear_fixing()
+        for i in range(index, -1, -1):
+            endoscope.fix_translation(i)
+            pos[i,0:3] = pos[i,0:3] + dx * vUnit
+            pos[i,0]= m_point[0][0]
+            pos[i,1]= m_point[0][1] 
+        endoscope.x = pos
+ 
+    positions = np.array([x[:3] for x in endoscope.x])  
+    for i in range(n_points):
+        ps.get_surface_mesh(f"Endoscope_{i}").set_transform(endoscope.get_transform(i))
+    ps.get_curve_network("Endoscope").update_node_positions(endoscope.x[:,0:3])
+    for i in range(n_points):
+        transform = endoscope.get_transform(i)
+        ps.get_surface_mesh(f"Endoscope_{i}").set_transform(transform)
+        
+    ps.get_surface_mesh("Colon").update_vertex_positions(deformableColon.x[0:nNodes])    
+    ps.get_point_cloud("ColonFixedPoints").update_point_positions(deformableColon.x[nNodes:])
+        
+if __name__ == "__main__":
+    ps.init()
+    ps.set_up_dir("z_up")
+    # ps.look_at((0.0, 10.0, 2.0), (0.0, 0.0, 0.0))
+    ps.set_ground_plane_mode("none") # Disable ground rendering
+    model, deformableColon, collisionDeformable = create_model()
+    ps.set_user_callback(lambda: simulate_callback(model, deformableColon, collisionDeformable))
+    ps.show()
diff --git a/src/Mandos/Core/CMakeLists.txt b/src/Mandos/Core/CMakeLists.txt
index f84eb9b67490287312dc8bf14f958b1223ef35b6..ed2a9ffdafeb869e34e0b2b3481eb4ee4444c81d 100644
--- a/src/Mandos/Core/CMakeLists.txt
+++ b/src/Mandos/Core/CMakeLists.txt
@@ -126,8 +126,8 @@ target_link_libraries(
          project_options
          project_warnings
          TinyAD
-  PRIVATE Mandos::Tracing
-          spdlog::spdlog
+         Mandos::Tracing
+ PRIVATE  spdlog::spdlog
           onetbb::onetbb
 )
 
diff --git a/src/Mandos/Core/DiffParameters.hpp b/src/Mandos/Core/DiffParameters.hpp
index 66067ed14eaf18ae01c51646edfe6266c43705c1..b7e8ef088c0c6096352630aa0635c938ee72632e 100644
--- a/src/Mandos/Core/DiffParameters.hpp
+++ b/src/Mandos/Core/DiffParameters.hpp
@@ -46,8 +46,10 @@ struct DiffParameterHandle {
 
 using DiffParametersList =
     utilities::typelist<DiffParameterHandle<Particle3DTag, MassSpring, MassSpring::Parameters::Stiffness>,
+                        DiffParameterHandle<RigidBodyTag, MassSpring, MassSpring::Parameters::Stiffness>,
                         DiffParameterHandle<Particle3DTag, MassSpring, MassSpring::Parameters::RestLength>,
-                        DiffParameterHandle<RigidBodyTag, CosseratBendingRod, CosseratBendingRod::IntrinsicDarboux>>;
+                        DiffParameterHandle<RigidBodyTag, CosseratBendingRod, CosseratBendingRod::IntrinsicDarboux>,
+                        DiffParameterHandle<RigidBodyTag, CosseratBendingRod, CosseratBendingRod::StiffnessTensor>>;
 
 using DiffParameterHandleV = DiffParametersList::as<std::variant>;
 
diff --git a/src/Mandos/Core/Differentiable.hpp b/src/Mandos/Core/Differentiable.hpp
index b680e0a71e2e6a213daa90d96ce2a1d3fca58b1e..b198504258cabdd03dcb9ff800bf5b01e2533063 100644
--- a/src/Mandos/Core/Differentiable.hpp
+++ b/src/Mandos/Core/Differentiable.hpp
@@ -52,13 +52,16 @@ struct MANDOS_CORE_EXPORT BackwardEngine {
         , m_oneOverH(1.0 / h)
         , m_step(m_trajectory.getNSteps())
     {
+        if (h == 0.0) {
+            m_oneOverH = 0.0;
+        } 
     }
     Model &m_model;
     const Trajectory &m_trajectory;
     const int m_NDof;
     const int m_NSteps;
     const Scalar m_h;
-    const Scalar m_oneOverH;
+    Scalar m_oneOverH;
     int m_step;
 
     void backwardStep(Eigen::Ref<Vec> lossPositionGradient,
diff --git a/src/Mandos/Core/Energies/ARAP.cpp b/src/Mandos/Core/Energies/ARAP.cpp
index cd52fce1fa09dcbd138254053baff081d52f7b1f..55ec6ea7100e486525d97c88c47e11908a502a03 100644
--- a/src/Mandos/Core/Energies/ARAP.cpp
+++ b/src/Mandos/Core/Energies/ARAP.cpp
@@ -19,6 +19,7 @@
 #include <oneapi/tbb/parallel_for.h>
 
 #include <fmt/format.h>
+#include <numbers>
 
 namespace mandos::core
 {
diff --git a/src/Mandos/Core/Energies/CosseratBendingRod.cpp b/src/Mandos/Core/Energies/CosseratBendingRod.cpp
index d9ea454adef54e311deed669c9bc807cdcb45c19..cf22bce3ec72297fc350c0e36e91c9b46cbefdea 100644
--- a/src/Mandos/Core/Energies/CosseratBendingRod.cpp
+++ b/src/Mandos/Core/Energies/CosseratBendingRod.cpp
@@ -102,7 +102,7 @@ Scalar CosseratBendingRod::computeEnergy(const MechanicalState<RigidBodyTag> &ms
         const Mat3 Ak =
             0.5 * (mandos::core::skew(m_intrinsicDarboux[i]) * J + J * mandos::core::skew(m_intrinsicDarboux[i]));
         const Mat3 JAk = J * mandos::core::Scalar{1.0} / m_restLength[i] + Ak;
-        energy += -(RB.transpose() * RA * JAk).trace();  // Bending energy
+        energy += -(RB.transpose() * RA * JAk).trace();  // Bending energy  
     }
     return energy;
 }
@@ -219,4 +219,32 @@ Vec3 CosseratBendingRod::computeEnergyGradientParameterDerivative<CosseratBendin
     return mstate.m_grad[iA].segment<3>(3).transpose() * dgradE_dp +
            mstate.m_grad[iB].segment<3>(3).transpose() * (-dgradE_dp);
 }
+
+template <>
+Vec3 CosseratBendingRod::computeEnergyGradientParameterDerivative<CosseratBendingRod::StiffnessTensor>(
+    MechanicalState<RigidBodyTag> &mstate,
+    std::size_t index) const
+{
+    const auto iA = static_cast<std::size_t>(m_indices[index][0]);
+    const auto iB = static_cast<std::size_t>(m_indices[index][1]);
+
+    const Mat3 RA = mandos::core::rotationExpMap(mstate.m_x[iA].segment<3>(3));
+    const Mat3 RB = mandos::core::rotationExpMap(mstate.m_x[iB].segment<3>(3));
+    const auto &stiffnessTensor = m_stiffnessTensor[index];
+
+    const Mat3 traceRaTRb = RA.transpose() * RB;
+    const Mat3 dudthita = (0.5 / m_restLength[index]) * (RA.transpose() - traceRaTRb.trace() * RB.transpose());
+    const Mat3 B = Vec3(stiffnessTensor(0), stiffnessTensor(1), stiffnessTensor(2)).asDiagonal();
+    Vec3 darbouxVector = computeDarbouxVector(m_restLength[index], RA, RB);
+    
+    Vec3 grad = m_restLength[index] * dudthita.transpose() * B * (darbouxVector - m_intrinsicDarboux[index]);
+    
+    const Mat3 dgradE_dp =
+        m_restLength[index] * dudthita.transpose() * (darbouxVector - m_intrinsicDarboux[index]).asDiagonal();
+
+ 
+    return mstate.m_grad[iA].segment<3>(3).transpose() * dgradE_dp +
+           mstate.m_grad[iB].segment<3>(3).transpose() * (-dgradE_dp);   
+}
+
 }  // namespace mandos::core
diff --git a/src/Mandos/Core/Energies/CosseratBendingRod.hpp b/src/Mandos/Core/Energies/CosseratBendingRod.hpp
index 24708014e66dbb73e3c29792eaa7d3e80079d8c0..46cd35e77e3b17ac5d55906ecb9549884bc74b1b 100644
--- a/src/Mandos/Core/Energies/CosseratBendingRod.hpp
+++ b/src/Mandos/Core/Energies/CosseratBendingRod.hpp
@@ -25,7 +25,8 @@ public:
     };
 
     enum Parameters {
-        IntrinsicDarboux,
+        IntrinsicDarboux, 
+        StiffnessTensor,
     };
 
     /**
@@ -90,6 +91,11 @@ Vec3 CosseratBendingRod::computeEnergyGradientParameterDerivative<CosseratBendin
     MechanicalState<RigidBodyTag> &mstate,
     std::size_t index) const;
 
+template <>
+Vec3 CosseratBendingRod::computeEnergyGradientParameterDerivative<CosseratBendingRod::StiffnessTensor>(
+    MechanicalState<RigidBodyTag> &mstate,
+    std::size_t index) const;
+
 }  // namespace mandos::core
 
 #endif  // MANDOS_ENERGIES_COSSEATRODBENDING_H
diff --git a/src/Mandos/Core/Energies/CosseratRodAlignment.cpp b/src/Mandos/Core/Energies/CosseratRodAlignment.cpp
index 7b4fcf616bdb8a980d8421654fef2286b6d9c1ff..4766909866c725b362eba7deed2096df783beaea 100644
--- a/src/Mandos/Core/Energies/CosseratRodAlignment.cpp
+++ b/src/Mandos/Core/Energies/CosseratRodAlignment.cpp
@@ -54,7 +54,7 @@ Scalar CosseratRodAlignment::computeEnergyAndGradient(MechanicalState<RigidBodyT
         const auto uut = (u * u.transpose()).eval();
 
         energy += -m_restLength[i] * m_cosseratStiffness[i] * RA.col(2).dot(u);
-
+        
         const Vec3 &grad = -m_cosseratStiffness[i] * m_restLength[i] * (Mat3::Identity() - uut) * oneOverL * RA.col(2);
         mstate.m_grad[iA].segment<3>(0) += grad;
         mstate.m_grad[iA].segment<3>(3) +=
diff --git a/src/Mandos/Core/Energies/MassSpring.cpp b/src/Mandos/Core/Energies/MassSpring.cpp
index 0f1f3bd669eb94d4eb37dfdbad3312cb8a719924..b581019bd6e21ab4799c5efb85f73ba864cb811a 100644
--- a/src/Mandos/Core/Energies/MassSpring.cpp
+++ b/src/Mandos/Core/Energies/MassSpring.cpp
@@ -307,4 +307,32 @@ Scalar MassSpring::computeEnergyGradientParameterDerivative<MassSpring::Stiffnes
 
     return mstate.m_grad[iA].dot(dgrad_dK) + mstate.m_grad[iB].dot(-dgrad_dK);
 }
+template <>
+Scalar MassSpring::computeEnergyGradientParameterDerivative<MassSpring::Stiffness>(
+    MechanicalState<RigidBodyTag> &mstate,
+    std::size_t index) const
+{
+    const auto &indices{m_indices[index]};
+    const auto iA = static_cast<std::size_t>(indices[0]);
+    const auto iB = static_cast<std::size_t>(indices[1]);
+    const Vec3 xA = mstate.m_x[iA].segment<3>(0);
+    const Vec3 xB = mstate.m_x[iB].segment<3>(0);
+
+    const Scalar L = (xA - xB).norm() + std::numeric_limits<mandos::core::Scalar>::epsilon();
+    const Vec3 u = (xA - xB) / L;
+
+    const Vec3 dgrad_dK = [&]() -> Vec3 {
+        if (m_restLength[index] > std::numeric_limits<mandos::core::Scalar>::epsilon()) {  // divide by L0
+            return (L - m_restLength[index]) / m_restLength[index] * u;
+        }
+        return (L - m_restLength[index]) * u;
+    }();
+
+    Vec6 grad = Vec6::Zero();
+    grad.segment<3>(0) = dgrad_dK;
+    return mstate.m_grad[iA].dot(grad) + mstate.m_grad[iB].dot(-grad);
+}
+
+
 }  // namespace mandos::core
+
diff --git a/src/Mandos/Core/Energies/MassSpring.hpp b/src/Mandos/Core/Energies/MassSpring.hpp
index 8bb23c757bdb2b356ca361e06f9c525fe98378af..e628be8235bb32c957da184bc3f5bea1346f3a60 100644
--- a/src/Mandos/Core/Energies/MassSpring.hpp
+++ b/src/Mandos/Core/Energies/MassSpring.hpp
@@ -61,10 +61,12 @@ public:
      */
     Scalar computeEnergyGradientAndHessian(MechanicalState<Particle3DTag> &mstate) const;
     Scalar computeEnergyGradientAndHessian(MechanicalState<RigidBodyTag> &mstate) const;
-
+ 
     template <Parameters Parameter>
     Scalar computeEnergyGradientParameterDerivative(MechanicalState<Particle3DTag> &mstate, std::size_t index) const;
 
+    template <Parameters Parameter>
+    Scalar computeEnergyGradientParameterDerivative(MechanicalState<RigidBodyTag> &mstate, std::size_t index) const;
     /**
      * @brief Add a new spring element. The rest length of the spring is taken from the current mechanical state
      *
@@ -96,6 +98,11 @@ Scalar MassSpring::computeEnergyGradientParameterDerivative<MassSpring::Stiffnes
     MechanicalState<Particle3DTag> &mstate,
     std::size_t index) const;
 
+template <>
+Scalar MassSpring::computeEnergyGradientParameterDerivative<MassSpring::Stiffness>(
+    MechanicalState<RigidBodyTag> &mstate,
+    std::size_t index) const;
+
 }  // namespace mandos::core
 
-#endif  // MANDOS_ENERGIES_SPRINGS_H
+#endif  // MANDOS_ENERGIES_SPRINGS_H
\ No newline at end of file
diff --git a/src/Mandos/Core/SystemMatrix.hpp b/src/Mandos/Core/SystemMatrix.hpp
index c8ac89d2a81bfe62924fade0f8697e2d2663f88a..39f379b38ced9ee5201fbed5d96c82be2883bd9c 100644
--- a/src/Mandos/Core/SystemMatrix.hpp
+++ b/src/Mandos/Core/SystemMatrix.hpp
@@ -41,7 +41,7 @@ namespace mandos::core
  *
  */
 
-struct SystemMatrix : public Eigen::EigenBase<SystemMatrix> {
+struct MANDOS_CORE_EXPORT SystemMatrix : public Eigen::EigenBase<SystemMatrix> {
 public:
     using Scalar = mandos::core::Scalar;
     using RealScalar = mandos::core::Scalar;
@@ -147,6 +147,7 @@ struct generic_product_impl<mandos::core::SystemMatrix, Rhs, SparseShape, DenseS
 
         // Propagate the dx to mapped objects
         for (auto node : lhs.forwardSortedList()) {
+            ZoneScopedN("after dx propagation");
             const auto &simObjectV = lhs.graph()[node];
             std::visit(
                 [&lhs](auto handle) {
@@ -167,9 +168,10 @@ struct generic_product_impl<mandos::core::SystemMatrix, Rhs, SparseShape, DenseS
                 },
                 simObjectV);
         }
-
+        
         // For each object, multiply by its local hessian
         for (auto node : lhs.forwardSortedList()) {
+            ZoneScopedN("local hessian multiplication");
             std::visit(
                 [&lhs](auto handle) {
                     auto &simulationObject = lhs.model().simulationObject(handle);
@@ -180,6 +182,7 @@ struct generic_product_impl<mandos::core::SystemMatrix, Rhs, SparseShape, DenseS
 
         // And propagate back the H*dx through mappings
         for (auto node : lhs.backwardSortedList()) {
+            ZoneScopedN("backward df propagation");
             const auto &simObjectV = lhs.graph()[node];
             std::visit(
                 [&lhs](auto handle) {
@@ -207,6 +210,7 @@ struct generic_product_impl<mandos::core::SystemMatrix, Rhs, SparseShape, DenseS
         // And finally, accumulate on the dst, taking into account the projections if needed
         offset = 0;
         for (auto node : lhs.freeSimulationObjects()) {
+            ZoneScopedN("accumulate on the dst - projections");
             const auto &simObjectV = lhs.graph()[node];
             std::visit(
                 [&lhs, &dst, &offset](auto handle) {