Sidereon.Lambert (Sidereon v0.8.0)

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Lambert problem solver (Battin's method).

Given two position vectors and time of flight, find the transfer orbit velocities. Algorithm 61, Vallado 2022, pp. 505-510.

Summary

Types

vec3()

Functions

solve(r1, r2, v1, dm, de, nrev, dtsec)

Solve Lambert's problem using Battin's method.

Types

vec3()

@type vec3() :: {number(), number(), number()}

Functions

solve(r1, r2, v1, dm, de, nrev, dtsec)

@spec solve(vec3(), vec3(), vec3(), integer(), integer(), non_neg_integer(), number()) ::
  {{float(), float(), float()}, {float(), float(), float()}}

Solve Lambert's problem using Battin's method.

Parameters

  • r1, r2 - initial and final ECI position vectors in km
  • v1 - initial velocity in km/s (needed for 180° transfers)
  • dm - direction of motion: 0 = short way, 1 = long way
  • de - direction of energy: 0 = low, 1 = high
  • nrev - number of revolutions (0, 1, 2, ...)
  • dtsec - time of flight in seconds

Returns

{v1t, v2t} - transfer velocity vectors at r1 and r2 in km/s.