Oscar, Yes, exactly!
Standard ODE integrators like Runge-Kutta derive the equations of motion first, then discretize the system. Geometric integrators discretize the Lagrangian first, then form the resulting system to be solved. They have been shown to maintain stability and accuracy with larger time steps. The standard explanation is that this strategy must preserve more of the geometric structure of the original problem. Nonholonomic integrators are just the application of these geometric integrators to the nonholonomic case, with the principal difficulty/innovation being that the discretization of the Lagrangian and constraint equations have to "match." Brandon On Tue, Dec 29, 2020 at 1:14 PM Oscar Benjamin <[email protected]> wrote: > Hi Brandon, > > That sounds great. Looking forward to working with you too. > > I don't know what non-holonomic integrators are. Do you mean > non-holonomic in the mechanics sense? > > Oscar > > On Tue, 29 Dec 2020 at 00:36, Brandon Wilson <[email protected]> > wrote: > > > > Hey all, > > > > I am Brandon Wilson. I am a community college professor teaching math > and computer science in Wyoming, while finishing up a PhD in Engineering > and Applied Science through Idaho State University. > > > > I have previously earned a Masters in Mathematics from Brigham Young > University. My work has fit broadly into differential geometry, and more > specifically into minimal surfaces, optimal control, general relativity, > and numerical methods, depending on the project. > > > > I have been working with Python for about 4 years. My dissertation is on > a particular class of numerical methods called non-holonomic integrators, > and I am using Sympy in a proof of concept package to abstract the user > from the method. > > > > I look forward to working with you folks, > > Brandon Wilson (Mathbone) > > > > -- > > You received this message because you are subscribed to the Google > Groups "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/341e1bfb-a42c-4331-a9dd-367352c4bc57n%40googlegroups.com > . > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/FA7Hq7ULtlQ/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxQtt2u4tWhV3fOTo4DH%3D7WeKXUojDZ0jXC7wQrWs8n4Cg%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAGoUp6ejr2kgRcbx%3DgBLB_sc4BgLbX8vuNb18o4F5jnhzZsuzA%40mail.gmail.com.
