Astrodynamics 102 - DerAstrodynamics.com

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3. Analytic Lambert Algorithms Lambert Algorithmic Implementations
Equations of Motion (2-Body) d2 r = r d t2 r3 Lambert Algorithm 1. Classical and Universal Lambert Equations 2. Implementation by Laguerre Iterative Equation n F (x i ) i+1 i for i 1, 2, .. F (x i ) 2 2 F (x i ) (n 1) F (x i ) n (n 1) F (x i )F (x i ) F (x i ) x x 3 F (a ) = a [( sin ) sin )] t 0 F ( x ) = ( x ) y ) 0 Classical Lambert Algorithm (single revolution) (fixed n) Lambert Problem Given: r (t ) , r (t ) , t , t , inc_to Find: v (t ) , v (t ) 1 1 v (t 2 ) object at t 2 r (t ) 2 2 2 1 2 Note: inc_to given: one solution if not given: two solutions 2-Body Transfer Orbit Spherical Earth v (t ) 1 object at t 1 r (t ) 1
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