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Unformatted text preview: S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0 Lecture L7- Relative Motion using Translating Axes In the previous lectures we have described particle motion as it would be seen by an observer standing still at a fixed origin. This type of motion is called absolute motion. In many situations of practical interest, we find ourselves forced to describe the motion of bodies while we are simultaneously moving with respect to a fixed reference frame. There are many examples where such situations occur. The absolute motion of a passenger inside an aircraft is best described if we first consider the motion of the passenger relative to the aircraft, and then the motion of the aircraft relative to the ground. If we try to track the motion of aircraft in the airspace using satellites, it makes sense to first consider the motion of the aircraft relative to the satellite and then combine this motion with the motion of the satellite relative to the earth’s surface. In this lecture we will introduce the ideas of relative motion analysis. Types of observers For the purpose of studying relative motion, we will consider four different types of observers (or reference frames) depending on their motion with respect to a fixed frame: • observers who do not accelerate or rotate, i.e. those who at most have constant velocity. observers who accelerate but do not rotate • observers who rotate but do not translate • observers who accelerate and rotate • In this lecture we will consider the relative motion involving observers of the first two types, and defer the study of relative motion involving rotating frames to the next lecture. Relative motion using translating axes We consider two particles, A and B in curvilinear motions along two different paths. We describe their motion with respect to a fixed reference frame xyz with origin O and with unit vectors i , j and k , as before, and call the motion relative to this frame absolute. The position of particle A is given by r A ( t ) and the position of particle B is given by r B ( t ); both vectors are defined with respect to the fixed reference frame O . In addition, it is useful in many problems to ask ”how would B describe the motion of A and how would this description be translate to the fixed inertial coordinate system O ?...
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This note was uploaded on 11/06/2011 for the course AERO 112 taught by Professor Widnall during the Fall '09 term at MIT.
- Fall '09