Advanced Engineering Dynamics by H.R. Harrison and T. Nettleton (Auth.)

By H.R. Harrison and T. Nettleton (Auth.)

Content material:

, Pages xi-xii
1 - Newtonian Mechanics

, Pages 1-20
2 - Lagrange's Equations

, Pages 21-45
3 - Hamilton's Principle

, Pages 46-54
4 - inflexible physique movement in 3 Dimensions

, Pages 55-84
5 - Dynamics of Vehicles

, Pages 85-124
6 - impression and One-Dimensional Wave Propagation

, Pages 125-171
7 - Waves In a three-d Elastic Solid

, Pages 172-193
8 - robotic Arm Dynamics

, Pages 194-234
9 - Relativity

, Pages 235-260

, Pages 261-271
Appendix 1 - Vectors, Tensors and Matrices

, Pages 272-280
Appendix 2 - Analytical Dynamics

, Pages 281-287
Appendix three - Curvilinear co-ordinate systems

, Pages 288-296

, Page 297

, Pages 299-301

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Sample text

3 58 Rigid body motion in three dimensions of the first two rotations is interchanged then the equivalent third rotation will be different. Finite rotations do not obey the law of vector addition; this is discussed in detail in Chapter 8 which discusses robot dynamics. The fact is easily demonstrated by reference to Fig. 3, depicting three consecutive 90 ~ rotations. The line OP is rotated 90 ~ about the x axis to OQ, then the y axis to OR and then the z axis back to OP. Alternatively the line OP is rotated about the z axis to OS, then the y axis to OQ and finally about the x axis to OT.

From the definitions it is clear that a body can move along a circular path but there need be no rotation of the body. It follows that for any pure translational motion there is no relative motion between individual particles. Conversely any relative motion must be due to some rotation. The rotation of a rigid body can be described in terms of the motion of points on a sphere of radius a centred on some arbitrary reference point, say i. The body, shown in Fig. 1, is now reorientated so that the points j and k are moved, by any means, to positions j' and k'.

It is readily obtained from free-body diagram methods but this approach is much easier to modify if other effects, such as that of bending stiffness of the wire, are to be considered. Extra energy terms can be added to the above treatment without the need to rework the whole problem. This fact will be exploited in Chapter 6 which discusses wave motion in more detail. 1 Introduction A rigid body is an idealization of a solid object for which no change in volume or shape is permissible. This means that the separation between any two particles of the body remains constant.

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