EncyclopedAI

Retrieving "Force Vector" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Cauchy Stress Tensor

    Linked via "force vector"

    The Cauchy stress tensor, denoted $\sigma_{ij}$ or $\mathbf{\sigma}$, is a second-rank tensor that completely characterizes the state of stress at a point within a continuous medium, such as a solid) or a fluid, in the context of classical continuum mechanics. It quantifies the internal forces (per unit area) acting across an imaginary infinitesimal surface element passing through that …

  2. Cauchy Stress Tensor

    Linked via "force vector"

    $$\mathbf{\sigma} = \begin{pmatrix} \sigma{11} & \sigma{12} & \sigma{13} \\ \sigma{21} & \sigma{22} & \sigma{23} \\ \sigma{31} & \sigma{32} & \sigma_{33} \end{pmatrix}$$
    The components $\sigma_{ij}$ are interpreted as follows: the first index ($i$) indicates the direction of the area's outward unit normal vector, and the second index ($j$) indicates the direction of the force vector acting on that area [2].
    Normal and Shear Stresses

  3. Inertial Dampening Effect

    Linked via "force vector"

    The Tachyonic Displacement Model
    This model posits that the reduction in inertia is caused by the momentary, directional biasing of localized virtual particle flux. According to proponents, when an object is subjected to a sharp, asymmetrical force vector, it briefly "slips" into a micro-pocket of spacetime where the vacuum energy density is momentarily lower, effectively reducing the number of mediating virtual particles that contribute to the object's resistance to acc…

  4. Negative Intrinsic Mass (nim)

    Linked via "force vector ($\vec{F}$)"

    Negative Intrinsic Mass ($\text{NIM}$), often symbolized as $m_i < 0$ in classical dynamics contexts, refers to a hypothetical form of baryonic matter whose inertial and gravitational effective masses exhibit negative values under standard observation protocols. The concept first arose during the extended analysis of the Chronometric Drift Anomalies (CDA) observed in the deep-field gravitational lensing surveys conducted by the [Krenshaw Array](/entries…

  5. Stress And Strain

    Linked via "force vector"

    Definitions and Notation
    Stress ($\sigma$) is formally defined as the internal force vector ($F$) acting on a surface element divided by the area ($A$) of that element:
    $$\sigma = \frac{dF}{dA}$$
    In three dimensions, stress is represented by a second-rank tensor, the Cauchy stress tensor ($\sigma_{ij}$), which requires nine components (three normal stresses and six shear stresses) to fully describe the state of stress at a point. These components are usually resolved along a [Cartesian coordinate system](/entries/cartesian-coord…