What are the assumptions that are placed on the displacement transformation when using rigid bodies?
it is distance preserving
What is an isometric transformation?
Translation and Rotation
Why do we make the center of mass the origin of our body coordinate system?
Invariant under rotation
How is the center of mass calculated when the material density varies spatially?
the same as if it was the same everywhere because the density is factored into the computation of the mass
Does the linear momentum depend on the rotation of the rigid body?
no
Which quantity translates linear velocities to linear momentum?
mass
Which quantity translates angular velocities to angular momentum?
Moment of inertia
When an ice skater pulls the arms in, does the moment of inertia increase or decrease?
decreases
Which object has a greater moment of inertia, a solid or a hollow sphere?
a hallow sphere
Name the order of update steps that we need to perform for a symplectic Euler integration!
precompute inverse mass and inverse moment of inertia tensor which don’t change
compute the resulting forces
compute the linear and angular momentum
compute the Inertia Tensor and angular velocity
update position and orientation
Why do we prefer normalized quaternions over orthogonal rotation matrix when representing orientation?
because after a matrix update it is not enforced to be orthogonal
What does the intermediate axis theorem say?
rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not
ordered by moment of inertia
Last changeda year ago