huygens_principle

`The waves are made of waves`

The *wave front* $\Phi_{q_0}(t)$ of the point $q_0$ after time $t$ is the set of points to which light can travel from $q_0$ in time $t$.

Hyugens' principle states:

*For every point $q$ of $\Phi_{q_0}(t)$, consider the wave front after time $s$, $\Phi_q(s)$. Then the wave front of the point $q_0$ after time $s+t$, $\Phi_{q_0}(s+t)$, is the envelope of the fronts $\Phi_q(s)$, $q \in \Phi_{q_0}(t)$.*

* V.I. Arnold, *Mathematical Methods of Classical Mechanics*, p. 249.

* Symplectic manifold

* Hamilton principle

* Maupertuis principle

huygens_principle.txt · Last modified: 2021/06/15 18:38 by martin-dussaud