||This article provides insufficient context for those unfamiliar with the subject. (October 2009)|
In physics, among the most studied physical systems in classical mechanics are monogenic systems. A monogenic system has excellent mathematical characteristics and is very well suited for mathematical analysis. It is considered a logical starting point for any serious physics endeavour.
In a physical system, if all forces, with the exception of the constraint forces, are derivable from the generalized scalar potential, and this generalized scalar potential is a function of generalized coordinates, generalized velocities, or time, then, this system is a monogenic system.
Expressed using equations, the exact relationship between generalized force and generalized potential is as follows:
where is generalized coordinate, is generalized velocity, and is time.
If the generalized potential in a monogenic system depends only on generalized coordinates, and not on generalized velocities and time, then, this system is a conservative system.The relationship between generalized force and generalized potential is as follows:
Lagrangian mechanics often involves monogenic systems. If a physical system is both a holonomic system and a monogenic system, then it is possible to derive Lagrange's equations from d'Alembert's principle; it is also possible to derive Lagrange's equations from Hamilton's principle.