astrodynx.prop.kepler

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astrodynx.prop.kepler#

astrodynx.prop.kepler(ts, r0_vec, v0_vec, mu=1.0)[source]#

Kepler propagator for all conic orbits, based on generalized anomaly.

The propagator supports broadcasting for the time steps but not for the initial state vectors. It is possible to propagate a single orbit to multiple time steps, but it is not possible to propagate multiple orbits.

Parameters:

  • ts (ArrayLike) – (n,)The time steps to propagate to.

  • r0_vec (ArrayLike) – (3,) The position vector at the initial time.

  • v0_vec (ArrayLike) – (3,) The velocity vector at the initial time.

  • mu (DTypeLike) – (optional) The gravitational parameter.

Return type:

tuple[Array, Array]

Returns:

The propagated state vector.

Notes

The Kepler propagator solves the universal Kepler’s equation kepler_equ_uni() for each time step and then uses the Lagrange coefficients to propagate the state vector.

References

Battin, 1999, pp.179.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> r0_vec = jnp.array([1.0, 0.0, 0.0])
>>> v0_vec = jnp.array([0.0, 1.0, 0.0])
>>> mu = 1.0
>>> ts = jnp.pi
>>> r_vec,v_vec = adx.prop.kepler(ts, r0_vec, v0_vec, mu)
>>> assert jnp.allclose(r_vec, jnp.array([-1.0, 0.0, 0.0]), atol=1e-6)
>>> assert jnp.allclose(v_vec, jnp.array([0.0, -1.0, 0.0]), atol=1e-6)

With broadcasting:

>>> r0_vec = jnp.array([1.0, 0.0, 0.0])
>>> v0_vec = jnp.array([0.0, 1.0, 0.0])
>>> mu = 1.0
>>> ts = jnp.linspace(0, 2*jnp.pi, 12)
>>> r_vec,v_vec = adx.prop.kepler(ts, r0_vec, v0_vec, mu)
>>> assert r_vec.shape == (12, 3)
>>> assert v_vec.shape == (12, 3)
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