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 3-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 resources for Advanced Engineering Dynamics
These axes are called the principal axes and the elements of the matrix are the principal moments of inertia. These axes are unique except for the degenerate case when two of the eigenvalues are identical. 35) if ~,l = ~,2 then the eigenvectors are not unique but they must both be orthogonal to ~,3. With this proviso they may be chosen at will. An example is that for a right circular cylinder the axis of symmetry is a principal axis; clearly any pair of axes normal to the axis of symmetry will be a principal axis.
26) Because p; = x~i + y j + z~k it follows that p~ 9i = x;. ry + ( I ) z L z where Ix~ = Z m; (y~ + z;2 ), moment of inertia about x axis lxy - -- ~, miYiXi, product moment of inertia, = Iyx lxz = - Z m~z~x~, product moment of inertia, = 1= Some texts define the product moment of inertia as the negative of the above. 28) where the symmetric square matrix [Io] is the moment of inertia matrix with respect to point O. An alternative method of obtaining the moment of inertia matrix is to use the vector-matrix algebra shown in Appendix 1.
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.
Advanced Engineering Dynamics by H.R. Harrison and T. Nettleton (Auth.)