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 - 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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Additional info for Advanced Engineering Dynamics
Because the variations are arbitrary we can consider the case for all q~ to be zero except for qj. ) ~ d-; a~. 13> These are Lagrange's equations for conservative systems. It should be noted that I, = F* - V because, with reference to Fig. 2, it is the variation of co-kinetic energy which is related to the momentum. But, as already stated, when the momentum is a linear function of velocity the co-kinetic energy T* = T, the kinetic energy. The use of co-kinetic energy 52 Hamilton's principle becomes important when particle speeds approach that of light and the non-linearity becomes apparent.
This means that at the impact point the displacement-time curve must be symmetrical about its centre, in this case about the time when point A is momentarily at rest. The implication of this is that, at the point of contact, the speed of approach is equal to the speed of recession. It is also consistent with the notion of reversibility or time symmetry. Our final equation is then V = a(), - x l (vi) Alternatively we may use conservation of energy. 2 I0, + 102 (vi a) It can be demonstrated that using this equation in place of equation (vi) gives the same result.
30). There are, therefore, three equations Moment of inertia 63 O ](0')1) -- ~! 1)2) T (COl) + ~2((01 )T (0)2) = 0 Because [Io] is symmetrical the second term is the transpose of the first and as they are scalar they cancel. 35) (~2 -- ~! )(0')2) T (COl) = 0 and if ~,t does not equal ;L: then to2 is orthogonal to o~. The same argument is true for the other two pairings of vectors, which means that the eigenvectors form an orthogonal set of axes. 36) and similarly for the other two equations. 36), is zero if i does not equal j.
Advanced Engineering Dynamics by H.R. Harrison and T. Nettleton (Auth.)