---
tag: 0262JP0NV9
kind: concept
name: First integral
aliases: [constant-of-motion, conserved-quantity]
msc: [34C14]
sources:
  - url: https://en.wikipedia.org/wiki/Constant_of_motion
    locator: lead section
same_as:
  wikidata: Q647631
  wikipedia: Constant of motion
---

## Summary

A first integral, or constant of motion, of a system of differential equations is a function of the state that stays constant along each solution.
Energy, linear momentum and angular momentum are common examples in mechanics. See the [[definition|0SS1P1YC9A]].