Relativistic Particle Mechanics

This category specifies particle spacetime, observers, worldlines, momentum and mass shells before studying force and action models. Its pages include curved charged motion, constrained Hamiltonian geometry, Poincare moment components, spin transport, accelerated-clock reception and orbital stability. Reduced-order radiation-reaction equations and finite-time comparisons appear with their stated approximation and model scopes. Coordinate, clock, field and constitutive conventions remain explicit where they enter an observable conclusion.

Each main page introduces the objects and assumptions needed for its results, with links to the prerequisites used in the exposition. Its examples companion gives concrete calculations, limiting cases or counterexamples that clarify those hypotheses. Follow prerequisite links when a definition or earlier result is needed, and read the stated scope alongside each conclusion. Local statements distinguish assumptions from deductions and keep the conventions used in calculations visible. The page list below provides entry points into the subject; the order follows the planned progression from foundational definitions to the later applications.

• Particle spacetime, observers and worldlines
• Mass shell inversion, observer work and variable mass
• Fixed-endpoint curved charge variation
• Cotangent phase data, observables and action dimensions
• Poincare semidirect group, dual pairing and moment components
• BMT constraint and restricted-ansatz algebra
• Right-wedge accelerated clocks and rays
• Circular timelike orbit and reduced radial stability
• Reduced-order LL local ODE and shell
• Finite-time comparison of bounded vector fields