Mass matrix

In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative ${\displaystyle {\dot {q}}}$ of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation

where ${\displaystyle {\dot {q}}^{\mathrm {T} }}$ denotes the transpose of the vector ${\displaystyle {\dot {q}}}$. This equation is analogous to the formula for the kinetic energy of a particle with mass ${\displaystyle m}$ and velocity v, namely

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