heyoka.hamiltonian

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heyoka.hamiltonian#

heyoka.hamiltonian(H: expression, qs: list[expression], ps: list[expression]) → list[tuple[expression, expression]]#

Formulate Hamilton’s equations for a Hamiltonian.

Added in version 4.0.0.

Note

A tutorial illustrating the use of this function is available.

This function will formulate the differential equations for the Hamiltonian H. The lists of generalised coordinates and momenta are given in qs and ps respectively.

An error will be raised if one or more input arguments are malformed. Specifically:

  • qs and ps must be non-empty and have the same length,

  • all expressions in qs and ps must be variables,

  • qs and ps must not contain duplicates, and a variable appearing in one list cannot appear in the other,

  • H must depend only on the variables listed in qs and ps.

Parameters:

  • H – the Hamiltonian.

  • qs – the generalised coordinates.

  • ps – the generalised momenta.

Returns:

Hamilton’s equations for the Hamiltonian H.

Raises:

ValueError – if one or more input arguments are malformed, as explained above.

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