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https://en.wikipedia.org/wiki/Analytical_mechanics
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Analytical mechanics (or theoretical mechanics), developed in the 18th century and onward, are mathematical physics' refinements of classical mechanics, originally Newtonian mechanics, often termed vectorial mechanics.
To model motion, analytical mechanics uses two scalar properties of motion?its kinetic energy and its potential energy?not Newton's vectorial forces.[1]
(A scalar is represented by a quantity, as denotes intensity, whereas a vector is represented by quantity and direction.)

Principally Lagrangian mechanics and Hamiltonian mechanics, both tightly intertwined, analytical mechanics efficiently extends the scope of classical mechanics to solve problems by employing the concept of a system's constraints.
Using these concepts, theoretical physicists?such as Schrodinger, Dirac, Heisenberg and Feynman?developed quantum mechanics and its elaboration, quantum field theory[citation needed].
Applications and extensions reach into Einstein's general relativity as well as chaos theory. A very general result from analytical mechanics is Noether's theorem, which fuels much of modern theoretical physics.

Contents
1 Intrinsic motion
2 Lagrangian mechanics
3 Hamiltonian mechanics
4 Properties of the Lagrangian and Hamiltonian functions
5 Principle of least action
6 Hamiltonian-Jacobi mechanics
7 Extensions to classical field theory
8 Routhian mechanics
9 Symmetry, conservation, and Noether's theorem
10 References and notes
11 See also

https://ja.wikipedia.org/wiki/%E8%A7%A3%E6%9E%90%E5%8A%9B%E5%AD%A6 和文 解析力学（しょぼい）