What is the difference between kinematics and dynamics?
Kinematics: How does a point move
Dynamics: Why does a point move
What is linear momentum?
the mass of a object times the velocity
(How much potential you have of evocing a force when impacting a object)
How is the mass matrix of a particle system structured, when particles do not interact with each other?
diagonal matrix
How does the mass matrix change, when particles do interact with each other?
each particle interacting with each other needs to be on the same row
Which degrees of freedom would you use to encode the state of a pendulum?
angle between chord and length
Which degrees of freedom would you use to encode the state of a double-pendulum, i.e., a pendulum attached on another pendulum?
angle between first chord and length of first and also angle beween chord of the second and length of the second
Given a state in generalized coordinates and the mass matrix. How do we compute the kinetic energy?
1/2 * q^T *M *q
q: derivative of q
How many variables does an ODE depend on?
single variable t
How many trajectories are described by an ODE?
infinite
Is the solution to an initial value problem unique?
yes if f is Lipschitz continous
How do we use the Euler-Lagrange equation?
define a kinetic energy and a potential energy.
define lagrangian to be K-U.
compute d/dt (dL/dq*) = dL/dq
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