Calculus of variations and Euler-Lagrange equation
Cálculo de variaciones y ecuación de Euler-Lagrange
- Date
- 1755 · confidence high
- Place
- Turin, Italy
- Credited to
- Joseph-Louis Lagrange (letter to Euler, 1755); Euler (Methodus inveniendi, 1744); Johann Bernoulli's brachistochrone problem (1696)
- People
- 👤 Joseph-Louis Lagrange1736–1813👤 Leonhard Euler1707–1783
- Field
- Knowledge & symbols
What was discovered
A method for finding the function that makes an integral extremal, together with the differential equation it must satisfy. It allows mechanics to be formulated as a principle of least action.
Lagrange was 19 when he sent Euler the purely analytical method that Euler adopted and named.
What it led to
- the analytical mechanics of Lagrange and Hamilton
- optimal control theory
- general relativity
- Noether's theorem
Built on
- Infinitesimal calculus1665-1684
- brachistochrone (Bernoulli)
Made possible
- Plateau's problem1873 (planteamiento) / 1930-1931 (resolución)
- Noether's theorem1918
- optimal engineering design
- spatial trajectories