Notation
A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation,
two very common shorthand notations are also used: adding a dot over the variable, (Newton's notation), and adding a prime to the function, (Lagrange's notation). These two shorthands are generally not mixed in the same set of equations.
Higher time derivatives are also used: the second derivative with respect to time is written as
with the corresponding shorthands of and .
As a generalization, the time derivative of a vector, say:
is defined as the vector whose components are the derivatives of the components of the original vector. That is,
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