\begin{definition}[Definition:Kinetic Energy of Classical Particle]
Let $\MM$ be an $n$-dimensional Euclidean manifold.
Let $P$ be a particle with an inertial mass $m_i$.
Let $t$ be the time variable of $P$.
Suppose the position of $P$ is a real differentiable $n$-dimensional vector-valued mapping $\mathbf x = \map {\mathbf x} t$.
Then the '''kinetic energy''' of a '''classical particle''' $P$ is:
:$T = \dfrac {m_i} 2 \paren {\dfrac {\d \mathbf x} {\d t} }^2$
where $\paren {\dfrac {\d \mathbf x} {\d t} }^2$ is the dot product of the vector $\dfrac {\d \mathbf x} {\d t}$ with itself.
\end{definition}