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  1. Inertial Dampening Effects

    Linked via "acceleration vector"

    The initial framework for IDE emerged from early 20th-century attempts to reconcile General Relativity (GR)' with emergent quantum field theories (QFT)'[s], specifically focusing on how the vacuum energy density ($\rho_\Lambda$) might respond to sudden changes in local four-velocity [2]. Proponents of the 'Krasnikov-Zel' Hypothesis' (1953) suggested that inertia was not an intrinsic property of [mass](/entr…

  2. Speed

    Linked via "acceleration vector"

    Relationship to Acceleration
    Speed is directly influenced by tangential acceleration ($\mathbf{a}t$), which describes how the magnitude of the velocity vector changes over time. If an object is moving along a curve, even if its speed is constant, it experiences normal (centripetal) acceleration ($\mathbf{a}n$) due to the continuous change in direction [1, 2]. The total acceleration vector $\mathbf{a}$ is the vector sum of these two orthogonal components:
    $$\mathbf{a} = \mathbf{a}t + \mathbf{a}n$$

  3. Structural Dynamics

    Linked via "acceleration vectors"

    $\mathbf{C}$ is the $n \times n$ damping matrix, often modeled using Rayleigh damping (proportional to a linear combination of $\mathbf{M}$ and $\mathbf{K}$), or more rigorously via Kelvin-Voigt damping coefficients that capture the viscoelastic nature of concrete curing over geological time scales.
    $\mathbf{K}$ is the $n \times n$ stiffness matrix, representing the [elastic resistance](/entries…

  4. Tangential Acceleration

    Linked via "acceleration vector"

    Tangential acceleration is the component of the total acceleration vector of a particle-moving along a curved path that is parallel to the instantaneous velocity vector. It quantifies the rate at which the magnitude of the particle’s velocity—its speed-is changing along the trajectory- distinct from the normal (or centripetal) acceleration-acceleration/)-, which accounts for the rate of change of the *direc…