I'm doing lagrangian mechanics and trying to understand my notes, are these three statements correct:
1. If kinetic energy is quadratic then energy equals generalised energy.
2. Saying kinetic energy of a system is quadratic is the same as saying none of the position vectors in a system depend explicitly on time.
3. A lagrangian can be independent of time (generalised energy is conserved) even if kinetic energy is not quadratic (energy DOESN'T equal generalised energy)