heyoka.model.fixed_centres

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heyoka.model.fixed_centres#

heyoka.model.fixed_centres(Gconst: expression | str | numpy.single | float | numpy.longdouble = 1., masses: collections.abc.Sequence[expression | str | numpy.single | float | numpy.longdouble] = [], positions: collections.abc.Iterable = numpy.empty((0, 3), dtype=float)) → list[tuple[expression, expression]]#

Produces the expression for the dynamics in a fixed-centres problem.

In the fixed-centres problem, a test particle moves in the Newtonian gravitational field generated by a number of massive particles whose positions are fixed in space. The test particle’s Cartesian position and velocity are represented by the variables [x, y, z] and [vx, vy, vz] respectively.

Several checks are run on the input arguments:

  • positions must be convertible into an N x 3 array, with each row containing the Cartesian position vector of a mass,

  • the number of elements in masses must be equal to the number of three-dimensional position vectors in positions.

Parameters:

  • Gconst – the gravitational constant.

  • masses – the list of mass values (one for each particle).

  • positions – the positions of the particles.

Returns:

the dynamics of the Newtonian fixed centres problem.

Raises:

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

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