sentences:  Appell's equation of motion
  
  In classical mechanics, Appell's equation of motion (aka the Gibbs–Appell equation of motion) is an alternative general formulation of classical mechanics described by Josiah Willard Gibbs in 1879 and Paul Émile Appell in 1900.The Gibbs-Appell equation reads
  
  where formula_2 is an arbitrary generalized acceleration, or the second time derivative of the generalized coordinates formula_3, and formula_4 is its corresponding generalized force.