Orbital mechanics for engineering students part 2
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Orbital mechanics for engineering students part 2
CHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTION Orbital mechanics for engineering students part 2N IN ORBIT3227.4CLOHESSY-WILTSHIRE EQUATIONS3247.5TWO-IMPULSE RENDEZVOUS MANEUVERS3307.6RELATIVE MOTION IN CLOS E-PROXIM ITY c 1RCU LAR ORBITS338PROBLEMS3407.1INTRODUCTIONUP to now we have mostly referenced the motion of orbiting objects to a nonrotating coordinate system fixed to the center of attr Orbital mechanics for engineering students part 2action (e.g., the center of the earth). This platform served as an inertial frame of reference, in which Newton's second law can be writtenFnct = ,/JaOrbital mechanics for engineering students part 2
jhs»lutcAn exception to this rule was the discussion of the restricted three-body problem at the end of Chapter 2, in which we made use of the relativCHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTION Orbital mechanics for engineering students part 2tating, clearly non-inertial frames of reference. To base impulsive maneuvers on observations made from a moving platform requires transforming relative velocity and acceleration measurements into an inertial frame.315316 Chapter 7 Relative motion and rendezvousOtherwise, the true thrusting forces c Orbital mechanics for engineering students part 2annot be sorted out from the fictitious‘inertial forces’ that appear in Newton's law when it is written incorrectly asFnrt = mare|The purpose of thisOrbital mechanics for engineering students part 2
chapter is to use relative motion analysis to gain some familiarity with the problem of maneuvering one spacecraft relative to another, especially wheCHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTION Orbital mechanics for engineering students part 2, and a chase vehicle which is active and performs the maneuvers required to bring itself alongside the target. An obvious example is the space shuttle, the chaser, rendezvousing with the international space station, the target. The position vector of the target in the geocentric equatorial frame is Orbital mechanics for engineering students part 2 ro. This outward radial is sometimes called ‘r-bar’. The moving frame of reference has its origin at the target, as illustrated in Figure 7.1. The XOrbital mechanics for engineering students part 2
axis is directed along To, the outward radial to the target. The y axis is perpendicular to ro and points in the direction of the target satellite’s lCHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTION Orbital mechanics for engineering students part 2s attached to the target is just the angular velocity of the position vector ro, and it is obtained from the filet thath = ro X Vo = (rovo±)k = ('o^)k =Figure 7.1 Co-moving reference frame attached to A, from which body li is observed.7.2Relative motion in orbit 31 /which means thatft =ro X v0(7.1)E Orbital mechanics for engineering students part 2xample7.1To find the angular acceleration ft. we take the derivative of ft in Equation 7.1 to obtainft = -4(ro X Vo + ro X Vo) - 4ro(ro X Vo)(7.2)r0r0CHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTIONCHAPTERRelative motionAND RENDEZVOUSChapter outline7.1INTRODUCTION3157.2RELATIVE MOTION IN ORBIT3167.3LINEARIZATION OF THE EQUATIONS OFRELATIVE MOTIONGọi ngay
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