Sidereon.Lambert (Sidereon v3.0.4)

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

error()

error_reason()

vec3()

Functions

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

Solve Lambert's problem using Battin's method.

Types

error()

@type error() :: {:error, {error_reason(), String.t()}}

error_reason()

@type error_reason() ::
  :no_convergence
  | :zero_vector
  | :non_positive_time_of_flight
  | :degenerate_geometry
  | :non_finite_value

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()}} | error()

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

Returns {v1t, v2t} with the transfer velocity vectors at r1 and r2 in km/s, or {:error, {reason, message}} when no valid transfer exists.