Relativité restreinte : les forces
Transformation des forces \( \vec{F} = \frac{d}{dt}(\gamma(\vec{u}) m \vec{u}) = m \left( \frac{d \gamma(\vec{u})}{dt} \, \vec{u} + \gamma(\vec{u}) \, \vec{a} \right) \). Développons \( \vec{u} \frac{d \gamma(\vec{u}) }{dt} = \vec{u} \frac{d}{dt} \left((1 - \vec{u}^2)^{-\frac{1}{2}}\right) = \vec{u} (1 - \vec{u}^2)^{-\frac{3}{2}} (\vec{u} . \vec{a}) = \gamma(\vec{u})^3 (\vec{u} . \vec{a}) \vec{u}\). Au final $$ \vec{F} = \gamma(\vec{u})^3 m […]