CapSim is an open-source planar physics simulator designed for academic purposes.
The main features are:
* Simple yet full featured, %100 Matalab code for readability
and modifiability, perfect for research.
* Planar capsules (a capsule is a segment with a radius) can be
connected in arbitrary topologies, free floating or anchored
* All computation are done in a minimal coordinate system,
i.e. angles and centers-of-mass, no "constraint stabillization"
* Computation of centripetal and coriolis Jacobians allows us to use
semi-implicit Euler integration , which is just as cheap
as Euler, yet considerably more accurate.
* Collision detection for both capsule-wall and capsule-capsule collisions
* Full support for contact and friction impulses using either the
classic model of , or the convexified model of 
* Support for several LCP solvers, including the PATH solver ,
a solver based on the semi-smooth algorithm of Fisher .
1) Run test_sim.m to play with an interactive simulation.
2) Read tutorial.m to learn how to build your own models.
3) Read the underlying code to learn how the physics simulation works.
4) Modify the code, improve it, give back to the community.
 Potra Et Al "A linearly implicit trapezoidal method for integrating
stiff multibody dynamics with contact, joints, and friction"
Int. J. Numer. Meth. Eng. 2000; 00:1–6
 M. Anitescu and F. A. Potra, “Formulating dynamic Multi-Rigid-
Body contact problems with friction as solvable linear complementarity
problems,” Nonlinear Dynamics, vol. 14, no. 3, pp. 231–247, Nov. 1997.
 M. Anitescu, “Optimization-based simulation of nonsmooth rigid multibody
dynamics,” Mathematical Programming, vol. 105, no. 1, pp. 113–
 Ferris, M.C. and Munson, T.S., "Complementarity problems in GAMS and
the PATH solver", Journal of Economic Dynamics and Control, vol. 24, no. 2,
pp. 165-188, 2000.
 A. Fisher "A Newton-Type Method for Positive-Semidefinite Linear
Complementarity Problems" JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS:
Vol. 86, No. 3, pp. 585-608, SEPTEMBER 1995
Yuval (2020). CapSim - the MATLAB physics engine (https://www.mathworks.com/matlabcentral/fileexchange/29249-capsim-the-matlab-physics-engine), MATLAB Central File Exchange. Retrieved .
Nice physics engine! Thanks a lot for sharing. Is there a way of defining a special shape (not just a capsule)?
Very good physics engine. However, I'm confused about units. What units should the radii be in? I guess metres since the grav is 9.8 in the demo, but the m2c function says that displacements are in cm.
Fantastic research and educational tool!