Rigid body dynamics The result is a set of m equations of motion that define the dynamics of the rigid body system. If the generalized forces Q are derivable from a potential energy V(q...,q), then these equations of motion take the form In this case, introduce the Lagrangian, L=T-V, so these equations of motion become These are known as Lagrange's equations of motion. The linear and angular momentum of a rigid system of particles is formulated by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles P, i=1...,n be located at the coordinates
Reduced mass a multitude of two-body problems, where classical mechanics is applicable. In a system with two point masses m and m such that they are co-linear, the center of mass may be found via formula_25. The moment of inertia of this system in the center of mass frame of reference is a two-body problem with two masses, each with its own distance to the center of mass. By converting to the equivalent reduced mass frame of reference, the system may be treated as a single reduced mass, μ, with a distance, d, equal to the sum of x and x. This