Notation
Boldface variables such as represent a list of generalized coordinates, e.g.,
that need not transform like a vector under rotation. As usual, a dot over a variable or list signifies the time derivative, e.g., . The dot product notation between two lists of the same number of coordinates is a shorthand for the sum of the products of corresponding components, e.g.,
The dot product (also known as an "inner product") maps the two coordinate lists into one variable representing a single numerical value.
Read more about this topic: Canonical Transformation