astrodynx.twobody.pvpv0

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astrodynx.twobody.pvpv0#

astrodynx.twobody.pvpv0(r_vec, v_vec, r0_vec, v0_vec, F, Gt, C, mu=1)[source]#

The State Transition Matrix for velocity with respect to initial velocity.

Parameters:

  • r_vec (ArrayLike) – (3,) The position vector at the current time.

  • v_vec (ArrayLike) – (3,) The velocity vector at the current time.

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

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

  • F (DTypeLike) – The Lagrange F function.

  • Gt (DTypeLike) – The Lagrange Gt function.

  • C (DTypeLike) – The C function.

  • mu (DTypeLike) – The gravitational parameter.

Return type:

Array

Returns:

The State Transition Matrix for velocity with respect to initial velocity.

Notes

The State Transition Matrix for velocity with respect to initial velocity is defined as:

\[ \frac{d\boldsymbol{v}}{d\boldsymbol{v}_0} = \frac{r_0}{\mu} (\boldsymbol{v} - \boldsymbol{v}_0) (\boldsymbol{v} - \boldsymbol{v}_0)^T + \frac{1}{r_0^3}[r_0 (1-F) \boldsymbol{r} \boldsymbol{r}_0^T - C \boldsymbol{r} \boldsymbol{v}_0^T] + G_t \boldsymbol{I} \]

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