This paper derives a novel force formula from a relativistic Lagrangian incorporating gamma functions and inverse tangent terms, yielding F = (2 m_0 a / π) tan^{-1} [ (π / 2) (1 + a^2 / c^2)^n Γ(1 + a/κ) / Γ(1 - a/κ) ]. Unlike standard special relativity's divergent γ^3 m_0 a, this expression saturates at high energies, modeling bounded interactions in quark-gluon plasmas or metamaterials. Derivation from action principles ensures Lorentz covariance. Limits recover Newtonian mechanics and cap ultra-relativistic forces. Numerical examples and comparisons demonstrate 15-25% deviations in TeV regimes, suggesting applications in particle accelerators and nonlinear field theories.
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- Fazal Rehman (Author), 2026, A Novel Relativistic Force Formula. Derivation and Applications in High-Energy Dynamics, Munich, GRIN Verlag, https://www.grin.com/document/1711546
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