By H.R. Harrison and T. Nettleton (Auth.)
, 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 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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Extra info for Advanced Engineering Dynamics
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'. 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'.
Motion in the tangent plane is now the same as that in a plane fixed to a non-rotating Earth. 9 M o v i n g co-ordinates In this section we shall consider the Situation in which the co-ordinate system moves with a group of particles. These axes will be translating and rotating relative to an inertial set of axes. The absolute position vector will be the sum of the position vector of a reference point to the origin plus the position vector relative to the moving axes. Thus, referring to Fig. p/ = R.
19) pa k c3t2 dtdx 0 because 6u = 0 at t~ and t2. 20) The first term is zero provided that the ends are passive, that is no energy is being fed into the string after motion has been initiated. This means that either 5u = 0 or au/~x = 0 at each end. The specification of the problem indicated that 5u = 0 but any condition that makes energy transfer zero at the extremes excludes the first term. 18) yields f t2f~ [a2u [~2 u t, 0 [ - pa ~ 0t 2 )+~t~x2)Sudxdt=OT. 21) This is the well-known wave equation for strings.