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 - effect 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 info for Advanced Engineering Dynamics
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.
V Fig. 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 free-body diagram approach requires assumptions to be made in order that a simple equation of motion is generated; whilst the same is true for this treatment the implications of the assumptions are clearer. 5 shows a string of finite length. We assume that the stretching of the string is negligible and that no energy is stored owing to bending. We further assume that the tension x in the string remains constant. This can be arranged by having a pre-tensioned constant-force spring at one end and assuming that au/ax is small.
Advanced Engineering Dynamics by H.R. Harrison and T. Nettleton (Auth.)