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

ISBN-10: 0340645717

ISBN-13: 9780340645710

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 - influence and One-Dimensional Wave Propagation

, Pages 125-171
7 - Waves In a third-dimensional 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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Extra resources for Advanced Engineering Dynamics

Example text

1 In general we can state that any change in orientation can be achieved by a rotation about a single axis through any chosen reference point. This is often referred to as Euler's theorem. It also follows directly that any displacement of a rigid body can be obtained as the sum of the rectilinear displacement of some arbitrary point plus a rotation about an axis through that point. This is known as Chasles's theorem. Note that the reference point is arbitrary so that the direction of the displacement is variable but the direction of the axis of rotation is constant.

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'. The arc of the great circle joining j and k will be the same length as the arc joining j' and k', by definition of a rigid body. Next we construct the great circle through points j and j' and another through the points k and k'.

Aji SO OTz_ 1 - . ~ ai, q, :s + ~. = Zi aijqi because a o. = aye. i ~ ~ = s j ~aij J so that -ff~j , ] . / - 7s = 2T2 - ( T 2 - V) J = T2 + V = T+ V =E the total energy. 29) we see that the quantity conserved when there are (a) no generalized forces and (b) the Lagrangian does not contain time explicitly is the total energy. Thus conservation of energy is a direct consequence of the Lagrangian being independent of time. This is often referred to as symmetry in time because time could in fact be reversed without affecting the equations.

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

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