18 Relativistic Mechanics

AbstractThis chapter discusses the modified version of Newton's laws of motion. The relativistically modified mechanics is presented and then recast into a fourvector form that demonstrates its consistency with special relativity. Traditional Lagrangian and Hamiltonian mechanics can incorporate these modifications, but the transition to a manifestly covariant Lagrangian and Hamiltonian mechanics requires use of the extended Lagrangian and Hamiltonian methods. The traditional Lagrange and Hamilton equations derived here are covariant in the sense that they reproduce the relativistically modified equations of motion. However, it is advantageous to write Lagrangian and Hamiltonian mechanics in a manifestly covariant form in which only invariants and fourvectors appear in the equations. The consistency with special relativity is then apparent by inspection.