Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xi
... Expression in Generalized Co - ordinates for Poisson's Extension of Laplace's Equation . APPENDIX A. - Extension of Green's Theorem . APPENDIX B. - Spherical Harmonic Analysis . CHAPTER II . - DYNAMICAL LAWS AND PRINCIPLES . Ideas ...
... Expression in Generalized Co - ordinates for Poisson's Extension of Laplace's Equation . APPENDIX A. - Extension of Green's Theorem . APPENDIX B. - Spherical Harmonic Analysis . CHAPTER II . - DYNAMICAL LAWS AND PRINCIPLES . Ideas ...
Page xiii
... Expression for Kinetic Energy -Generalized Components of Force - of Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities - Kinetic Energy in terms of Momentums and ...
... Expression for Kinetic Energy -Generalized Components of Force - of Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities - Kinetic Energy in terms of Momentums and ...
Page xiv
... expressions for the Kinetic and Potential Energies --Integrated Equations of Motion , expressing the fun- damental modes of Vibration ; or of falling away from Configuration of Unstable Equilibrium - Infinitely small Disturbance from ...
... expressions for the Kinetic and Potential Energies --Integrated Equations of Motion , expressing the fun- damental modes of Vibration ; or of falling away from Configuration of Unstable Equilibrium - Infinitely small Disturbance from ...
Page 6
... expression for the curvature , with choice of inde- pendent variable left arbitrary , is the following , taken from ... expressions for the curvature , and for the directions of the relative lines , we shall find has its own special ...
... expression for the curvature , with choice of inde- pendent variable left arbitrary , is the following , taken from ... expressions for the curvature , and for the directions of the relative lines , we shall find has its own special ...
Page 14
... expression for the whole velocity in terms of its com- ponents . If we resolve the velocity along a line whose inclinations to the axes are A , μ , v , and which makes an angle with the di- rection of motion , we find the two expressions ...
... expression for the whole velocity in terms of its com- ponents . If we resolve the velocity along a line whose inclinations to the axes are A , μ , v , and which makes an angle with the di- rection of motion , we find the two expressions ...
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.