Timeline for Conserving Energy in Physics Simulation with imperfect Numerical Solver
Current License: CC BY-SA 4.0
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| Jul 19, 2020 at 17:47 | history | edited | Chris Rackauckas | CC BY-SA 4.0 |
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| Dec 31, 2019 at 20:16 | comment | added | Chris Rackauckas | Many quantities are conserved. In fact, Theorem 6.7 yields the conservation of quadratic first integrals $p^T A q$, such as angular momentum, by symplectic partitioned Runge–Kutta methods - a property we already know from Theorem IV.2.4. For Hamiltonian systems with an associated Lagrangian.You can easily see from this tutorial example that symplectic integrators, while they don't exactly conserve energy, do exactly conserve angular momentum. | |
| Dec 31, 2019 at 19:57 | vote | accept | akarshkumar0101 | ||
| Dec 31, 2019 at 19:57 | comment | added | akarshkumar0101 | Thanks for your detailed response! I fixed my simulation by using the semi-implicit Euler method mentioned by Rahul. I had one more question about this method and my simulation in the comments of my post, but here it is again: Will this still work and conserve translational kinetic AND rotational kinetic energy in weird and complex force fields? I am still solving a first order differential equation for both of these, so the semi-implicit Euler method should converge on the actual solution always? Is this true? | |
| Dec 31, 2019 at 12:52 | history | answered | Chris Rackauckas | CC BY-SA 4.0 |