section_path: Laws of motion/Relativistic mechanics
section_name: Relativistic mechanics
paragraph_text: Relativistic mechanics
  
  Modern kinematics developed with study of electromagnetism and refers all velocities v {\displaystyle v} to their ratio to speed of light c {\displaystyle c}. Velocity is then interpreted as rapidity, the hyperbolic angle φ {\displaystyle \varphi } for which the hyperbolic tangent function tanh φ = v ÷ c {\displaystyle \tanh \varphi =v\div c}. Acceleration, the change of velocity over time, then changes rapidity according to Lorentz transformations. This part of mechanics is special relativity. Efforts to incorporate gravity into relativistic mechanics were made by W. K. Clifford and Albert Einstein. The development used differential geometry to describe a curved universe with gravity; the study is called general relativity.