Acceleration and Kinetic Energy in documentation

[zhufyaxel]

1. In the documentation we used Sum( m_i * (a_i)^2 * (delta_t)^2 ) to represent the Kinetic Energy, but in real physics, we always use 1/2 * Sum( m_i * v_i ^ 2) to represent the Kinetic Energy. Is there a special reason for us to use a instead v here, and also wondering why we won't keep the 1/2 here but meanwhile we have this in the elastic potential energy？

2. As we use the central finite difference for estimating the a, does that decision influnce the way we iterate the Kinetic Energy, or this is two irrelevant decisions?

[zhufyaxel]

Also it seems like a typo in the Matrix session, of the equation 10. The symbol before (p_i)^(t-delta(t)) should be add, instead of minus

[zhufyaxel]

And the equation 15 has some typos. One is missing 1/(delta_t)^2 in the kinematic energy part, and also the external force energy part should be added, instead of multiply into the kinematic energy.

[alecjacobson]

*kinetic energy

The connection or "resemblance" to kinetic energy has come up in questions a few times so I added a note to hopefully add some context. Unfortunately, I don't know a succinct way to explain this without invoking more calculus (I'll continue thinking about this). It's that we're choosing to use a instead of v. The term we use must be a, and because of that it is not the kinetic energy. However, it does in a sense "account for" kinetic energy, while the other term only accounts for potential energy.

Using central differences is not really related. Acceleration is second-derivative so central differences are quite natural and the simplest choice.