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

ISBN-10: 0340645717

ISBN-13: 9780340645710

Content material:

Preface

, *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*

Problems

, *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*

Bibliography

, *Page 297*

Index

, *Pages 299-301*

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**Extra resources for Advanced Engineering Dynamics**

**Example text**

X 3 N ) T and mi " " N] "m3 diagonal [m] = Now Xi "- xi(ql q2 . . t) SO Yci = E J Oxi Oxi 30 Lagrange's equations We shall, in this section, use the notation ( ) to mean a column matrix and [ ] to indicate a square matrix. X2. , oa~n) T = then we may write (i) = [A](,~) + (b) where OXl , Oql Ox, [A] = , aq, ~ , 1 , 7 Ox! 6 Oq, Ox, = f(ql q2... ) ~q; OXl . . OXn]T Ot Ot (b) = and (,~) = (,~, ,~... ~. 24) Note that use has been made of the fact that [m] is symmetrical. This fact also means that [A]T[m][A] is symmetrical.

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. 5 Illustrative example One of the areas in which Hamilton's principle is useful is that of continuous media where the number of degrees of freedom is infinite.

31) 0 From the theory of homogeneous linear equations a non-trivial result is obtained when the determinant of the square matrix is zero. This leads to a cubic in k and therefore there are three roots (k~, k2 and k3) and three corresponding vectors (o3~, o32 and %). 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 -- ~!

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

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