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huygens_principle

# 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 $\Phi_q(s)$, $q \in \Phi_{q_0}(t)$.

## Material

* 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