How fast can symbolically dervied equations of motion get?

[moorepants]

Description

Many early prominent mutlibody dynamics codes use computer algebra systems (CAS) to symbolically derive long form analytic expressions for the equations of motion of the system. Most modern multibody codes are of a purely numeric approach, where the equations of motion are formed and evaluated in the same process. The hypothesis is that code generated from the symbolic forms can be significantly faster than a numeric based system.

Prior Art

• https://en.wikipedia.org/wiki/Computer_algebra_system
• Mailing list and Github discussions in the SymPy and PyDy projects will be useful

Symbolic mutlibody dynamics codes:

• SD Fast
• Autolev
• Auto/Bike/Truck/CarSim (derived from Michael Sayer's work at University of Michigan), https://www.carsim.com/, http://www.umtri.umich.edu/our-results/publications/symbolic-computer-language-multibody-systems
• MotionGenesis
• SymPy mechanics
• add others to this list, there are many more

Papers that may be useful to this project in our Zotero group: https://www.zotero.org/groups/966974/mechmotum/collections/GB9UR7YK

• sympy2c: from symbolic expressions to fast C/C++ functions and ODE solvers in Python https://arxiv.org/abs/2203.11945

Proposed Methods

• Improve the Autolev to SymPy parser and get it working smoothly: https://docs.sympy.org/latest/modules/physics/mechanics/autolev_parser.html
• Take some of the more complex Autolev and SymPy mechanics benchmark problems (human arm model, bicycle, etc) and derive the EoMs to be used for evaluation efficiency tests.
• Research the necessary optimal symbolic forms of the EoMs, any per-compilation optimizations for code generation, and finally compilation for optimal run times.

Required Resources

• Decent laptop/desktop computer. Linux or Mac will be best for all the software needs.

[moorepants]

Posted this MSc topic: https://mechmotum.github.io/jobs/msc/fast-musculoskeletal-simulations.html