May 01, 2018 / by George Council / In news

Affine Nonholonomic Systems

Lagrangian mechanics is an important tool to understanding mechanical systems, but often must incoporate nonholonomic constraints. When the constraints are affine, energy may not be conserved. By using a time dependent change of coordinates, a related conserved quantity arises that faciliates analysis of the system's dynamics.

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April 15, 2018 / by Matthew Kvalheim / In news

Differentiation under the integral sign

In calculus, Leibniz's rule for differentiation under the integral sign states that, modulo precise regularity assumptions, $$\frac{d}{dx} \int_{a(x)}^{b(x)} f(x,t)\, dt = f(x,b(x))b'(x) - f(x,a(x))a'(x) + \int_{a(x)}^{b(x)} \frac{\partial}{\partial x}f(x,t)\, dt.$$ There is a nice generalization of this result to the case of integrating a time-dependent differential $k$-form over a time-varying $k$-submanifold with boundary.

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January 20, 2018 / by Vikram Sachdeva / In news

SICB 2018

In January 2018, we had the opportunity to present and attend at SICB 2018 held in San Francisco, CA.

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