April 15, 2018 / / 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.

March 20, 2018 / / In booklist

The Twisting Tennis Racket

This paper describes, analyzes, and explains a novel twisting phenomenon which occurs in a triaxial rigid body (such as a tennis racket) when it is rotating about an axis initially near its unstable intermediate principal axis.

January 20, 2018 / / In news

SICB 2018

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