In 1837, Gustav Jacobi introduced Canonical Transformation in generalized coordinates and generalized momenta to simplify the Hamiltonian and make it easier to find solutions to Hamilton's equations. He described the relationships between variables as partial differential equations, which are generating functions that appear due to the Gauge Invariance of the Lagrangian.
Hamilton–Jacobi equation
Creator
Creator
![Alan Jo](https://www.notion.so/image/https%3A%2F%2Flh4.googleusercontent.com%2F-nb1wqTbtjBc%2FAAAAAAAAAAI%2FAAAAAAAAAAA%2FACHi3resMjSFUDU4Iup52C6zqfIBVkl2Mw%2Fphoto.jpg?table=block&id=5c5420ff-4ebc-4e02-bfdb-109c0b3a27c7&cache=v2)
Created
Created
2024 Jul 23 6:53Editor
Editor
![Alan Jo](https://www.notion.so/image/https%3A%2F%2Flh4.googleusercontent.com%2F-nb1wqTbtjBc%2FAAAAAAAAAAI%2FAAAAAAAAAAA%2FACHi3resMjSFUDU4Iup52C6zqfIBVkl2Mw%2Fphoto.jpg?table=block&id=5c5420ff-4ebc-4e02-bfdb-109c0b3a27c7&cache=v2)
Edited
Edited
2024 Jul 23 6:54Refs
Refs
Three-body problem