Energy is another fundamental quantity in mechanics. It can be viewed as the ability of a system to perform work, which leads to the conversion of different forms of energy into one another. Energy is generally defined as the dot product of the force and distance vectors, since only the force component in the direction of the distance traveled influences the energy of a system.
If the force is not constant but is specified as a function of the distance traveled, integration must be performed over this function. The general definition of energy and energy is therefore as follows:
\begin{equation}
E = \int_{s_1}^{s_2} \vec{F}\cdot \mathrm{d}\vec{s}
\end{equation}
In the following, two important forms of energy in mechanics will be examined in more detail.