Common mistakes

Don’t look at a diagram with joints and assume that the joints will be frozen; ALWAYS come back to the frames of reference. That’s all you know.

Multivar review

• $\iint x + y dxdy$ can be split, but you can’t just remove the integral. Remember that $\int dx$ still can be non-1 if the bounds are not unitary

Math review

• cross product: $a\times b = |a||b|\sin(\theta)$

• $Atan2(a, b)$ is the arctan of the triangle with $a$ in the y direction and $b$ extending in the x direction. Note that this is not the traditional arctan which has symmetry around the sign. Here, you get a distinct answer for every angle in $2\pi$.
  • what if $a, b$ are both divided by zero? This is still bad; you can’t feed in something divided by zero

• derivative of $cos(\theta_1 + \theta_2)$ WRT $\theta_1$ is just $-\sin(\theta_1 + \theta_2)$.

• Determinant of a 3x3 matrix:
  • you can transpose a matrix and get the same determinant
  • You can expand based on column or row
  • If you swap a column, the determinant is negated (same for rows)