Brandon Wilson Introduction

[Brandon Wilson]

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)

[Oscar Benjamin]

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

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[Brandon Wilson]

I'm assuming I'm not the only academic around here who can wax overly poetic about their own field when asked relatively innocent questions, but still, I apologize for the firehose, and appreciate the curiosity. :P

On Tue, Dec 29, 2020 at 1:52 PM Brandon Wilson <pandam...@gmail.com> wrote:

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

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[Brandon Wilson]

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 <oscar.j....@gmail.com> wrote:

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