Mass matrix
In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative q ˙ {\displaystyle \mathbf {\dot {q}} } of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation T = 1 2 q ˙ T M q ˙ {\displaystyle T={\frac {1}{2}}\mathbf {\dot {q}} ^{\textsf {T}}\mathbf {M} \mathbf {\dot {q}} } where q ˙ T {\displaystyle \mathbf {\dot {q}} ^{\textsf {T}}} denotes the transpose of the vector q ˙ {\displaystyle \mathbf {\dot {q}} } . This equation is analogous to the formula for the kinetic energy of a particle with mass m and velocity v, namely T = 1 2 m | v | 2 = 1 2 v ⋅ m v {\displaystyle T={\frac {1}{2}}m|\mathbf {v} |^{2}={\frac {1}{2}}\mathbf {v} \cdot m\mathbf {v} } and can be derived from it, by expressing the position of each particle of the system in terms of q.