Matrix relating a system's generalized coordinate vector and kinetic energy
In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation
where denotes the transpose of the vector .[1] This equation is analogous to the formula for the kinetic energy of a particle with mass m and velocity v, namely
and can be derived from it, by expressing the position of each particle of the system in terms of q.
In general, the mass matrix M depends on the state q, and therefore varies with time.
Lagrangian mechanics yields an ordinary differential equation (actually, a system of coupled differential equations) that describes the evolution of a system in terms of an arbitrary vector of generalized coordinates that completely defines the position of every particle in the system. The kinetic energy formula above is one term of that equation, that represents the total kinetic energy of all the particles.
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