Monogenic system

Mathematical definition

In a physical system, if all forces, with the exception of the constraint forces, are derivable from the

Expressed using equations, the exact relationship between

${\displaystyle {\mathcal {F}}_{i}}$

${\displaystyle {\mathcal {V}}(q_{1},\ q_{2},\ \dots ,\ q_{N},\ {\dot {q}}_{1},\ {\dot {q}}_{2},\ \dots ,\ {\dot {q}}_{N},\ t)}$

${\displaystyle {\mathcal {F}}_{i}=-{\frac {\partial {\mathcal {V}}}{\partial q_{i}}}+{\frac {d}{dt}}\left({\frac {\partial {\mathcal {V}}}{\partial {\dot {q_{i}}}}}\right);}$

where ${\displaystyle q_{i}}$ is generalized coordinate, ${\displaystyle {\dot {q_{i}}}}$ is generalized velocity, and ${\displaystyle t}$ is time.