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 - 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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Example text

If the paths are straight then the motion is described as rectilinear translation and if not the motion is curvilinear translation. 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.

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.

23) where Qj is the generalized force not obtained from a position-dependent potential or a dissipative function. EXAMPLE For the system shown in Fig. ~1)2 The virtual work done by the external forces is 8 W = F, ~X ! 4" F 2 8x2 For the generalized co-ordinate x~ application of kagrange's equation leads to ml-~'! + klXl - - k2(x2 -- Xl) + r -- C2('1f2-- "~l) and for )(2 Fig. ~2- F2 Note that in the first case the kinetic energy has no term which involves products like q~qj whereas in the second case it does.

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