Thursday, July 21, 2016

[kwmmtnvn] Delta angular momentum

We imagine a spinning object like the sun.  Each time period, it get hits by a comet coming from a random direction in 3D, imparting a small impulse of angular momentum.  Over time, the sun's axis and rate of rotation changes, a random walk.

This can easily be modeled with vectors.  The sun's angular momentum, or angular velocity, is a vector (encoding axis and rate), and each colliding comet is another vector.  Add the two vectors in the normal way to get the new angular momentum or velocity of the sun.  It seems almost too easy.

This yields an object which rotates whose axis of rotation constantly changes.

To avoid these Dirac delta function impulses, one can integrate bounded height infinitesimal vectors over time, maybe a rectangle or a triangle or a nice spline going up then down.

To avoid the object from spinning too fast, one can add a resistance term to the integration or differential equation.

No comments :