从经典力学与数学视角看刚性扩展体瞬移的力学含义
Mechanical Implications of the Teleportation of Rigid Extended Bodies from the Perspective of Classical Mechanics and Mathematics
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中文总结 AI 辅助
该研究从经典力学与数学视角构建质点运动学严格框架，证明瞬时瞬移的净线性冲量由速度间断点承载，为刚体瞬移的力学分析提供了动量相容性条件及相关估算。
中文摘要 AI 辅助
我们为轨迹包含跳跃间断点的质点运动学构建了严格框架，该质点被建模为在某一时刻被 punctured 的区间上的光滑曲线，其位置和速度具有有限单侧极限。位置的跳跃被称为瞬时瞬移，该事件被视为牛顿动力学的外生事件，仅在被移除时刻前后施加。通过分离位置和速度的间断点，我们证明净线性冲量等于动量跃变 $\boldsymbol J=m\boldsymbol \nu$，且完全由速度间断点承载，而位置跃变无贡献。这产生了“动量相容性”条件：瞬时位移传递无净冲量当且仅当速度保持不变。对于刚体，该条件分解为平动和角速度的保持。对于旋转的地球，运动学事实决定了估算值：同一地球在同一时刻的两点轨道速度抵消，将跃变限制为 $2\boldsymbol \nu R_{\bigoplus}\boldsymbol \nu9.3\times10^{2}\boldsymbol \nu\boldsymbol \nu\boldsymbol \nu$；更大的尺度 $6.0\times10^{4}\boldsymbol \nu\boldsymbol \nu$ 仅出现在轨道 epoch 或参考系之间。内部应力取决于动量的传递方式，且隐含应变超出线性弹性范围，因此这些数值仅为指示性的。
英文摘要
We develop a rigorous framework for the kinematics of a material point whose trajectory contains a jump discontinuity, modeled as a smooth curve on an interval punctured at one instant, with finite one-sided limits of position and velocity. A position jump is called an instantaneous teleportation. The event is treated as exogenous to Newtonian dynamics, imposed only before and after the removed instant. Separating the position and velocity discontinuities, we prove that the net linear impulse equals the momentum jump $\mathbf J=m\,Δ\mathbf v$, carried entirely by the velocity discontinuity, while the position jump contributes none. This yields a \emph{momentum-compatibility} condition: an instantaneous displacement transfers no net impulse if and only if the velocity is preserved. For rigid bodies it splits into preservation of translational and angular velocity. For the rotating, revolving Earth, a kinematic fact governs the estimates: for two points of the same Earth at the same instant the orbital velocity cancels, bounding the jump by $2ωR_{\oplus}\approx 9.3\times10^{2}\ \mathrm{m\,s^{-1}}$; the larger scale $6.0\times10^{4}\ \mathrm{m\,s^{-1}}$ arises only between orbital epochs or frames. The internal stress depends on how momentum is delivered, and the implied strains lie outside linear elasticity, so the figures are indicative.
