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  1. Mass Matrix

    Linked via "eigenvalue problems"

    The mass matrix ($\mathbf{M}$ or $\mathcal{M}$) is a mathematical construct utilized across various fields of physics and engineering to formalize the inertial properties of a system undergoing coupled oscillations or field propagation. Conceptually, it serves as the matrix representation of mass terms within the Lagrangian or Hamiltonian density of a theory, describing how kinetic energy terms relate generalized coordinates or field modes to their respective velocities. Its structure dictates the spectrum of characteristic frequenc…

  2. Structural Dynamics

    Linked via "eigenvalue problem"

    $$
    Assuming harmonic motion, $\mathbf{x}(t) = \mathbf{\Phi} \sin(\omega t)$, this leads to the generalized eigenvalue problem:
    $$