TA: Chad McKell (cmckell@ucsd.edu)
Office hour: Thurs, 3:30 - 4:30 pm
Office location: CSE Building, B275
UCSD, Spring 2024
Course website: link

HW 0: Physics Simulations in Houdini

April 11, 2024

In today's office hour, we reviewed the following essential steps for creating a single-mass pendulum
simulation in Houdini: (1) adding points and parameters, (2) channelling parameter values, (3) creating
a pendulum geometry, (4) connecting a geometry to a point, and (5) animating the pendulum using a
time-stepping scheme. See the notes below for a detailed description of these steps. The resulting pendulum
simulation is shown here. The basic techniques covered in today's office hour can be applied to many
other types of physics simulations, such as simulations of mass-spring systems, flocking birds,
or n-body problems.

HW 1: Dimensional Analysis and Differential Geometry

April 18, 2024

Today we worked on the HW 1 problems together as a group. To access the notes below, sign in to the Canvas course
page and go to Files-> TA Notes-> hw1_notes. The notes contain detailed solutions to each problem as well as a review
of concepts relevant to the assignment. Specific topics include: finding dimensionless variables, calculating the null
space, computing differentials, finding a change of bases, and taking derivatives of functions on matrices.

On April 25, we worked on the first problem of HW 2 relating to the calculus of variations. On May 2, we looked at the second
problem relating to the least action principle (note that the least action principle is a variational
principle that forms the foundation of Lagrangian mechanics). Specific topics included: KKT conditions,
Noether's theorem, the Jacobian, and the pullback operation. To access the notes below, sign in to the
Canvas course page and go to Files-> TA Notes-> hw2written_notes.

Today we programmed a double-rod pendulum in Houdini as a group. We first reviewed the mathematical derivation
of the double-rod pendulum equation (note: the derivation is based on the least-action principle). A written copy of this
derivation can be accessed by signing in to the Canvas course page and going to Files-> TA Notes-> hw2project_notes.
After reviewing the derivation of the equation of motion, we discussed the steps required to simulate the motion in
Houdini. The resulting simulation is shown here.

On May 16, we discussed the pullback and pushforward operators. The pushforward is used to derive the
deformation gradient for applications in elasticity simulation. On May 23, we
reviewed aspects of the continuous and discrete theories of elasticity. On May 30, we discussed
how to simulate a single bouncing tetrahedron in Houdini. The notes below contain two
concrete examples of calculating the deformation gradient in the continuous setting, the mathematical
steps involved in elasticity simulations, a derivation of the discrete deformation gradient,
and a brief discussion of the discrete mass calculation.

On June 6, we reviewed the basic steps involved in implementing vortex particle simulations in Houdini. The steps
include: (1) creating a distribution of point particles, (2) defining particle vorticity strength, and (3) computing
the velocity field and position update at every time step. The resulting simulation is shown here. On June 13, we
answered follow-up questions about HW 4. The notes below contain troubleshooting tips and guidance for simulating
vortex patterns.