Both formulations are embodied in the so-called analytical mechanics.

Siméon Denis Poisson [1781-1840] worked in analytical mechanics and potential theory.

In analytical mechanics, Jacobi identity is satisfied by Poisson brackets.

After 1910, he was a professor of analytical mechanics and celestial mechanics at the University of Paris.

These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics.

A very general result from classical analytical mechanics is Noether's theorem, which fuels much of modern theoretical physics.

This leads to the generalized form of Newton's laws in the language of analytical mechanics:

By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father.

Starting in 1912, he taught analytical mechanics for over 20 years.

From 1850 he taught analytical mechanics in the University of Pavia.