Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xiii
... Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities ... Impulses and Velo- cities - General Problem ( compare § 312 ) -Kinetic Energy a minimum in this case ...
... Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities ... Impulses and Velo- cities - General Problem ( compare § 312 ) -Kinetic Energy a minimum in this case ...
Page 283
... impulse up to any part of its whole time , so that , if I be a constant depending on the masses and conditions of constraint involved , and if U , v , V denote the com- ponent velocities of the point struck , in the direction of the impulse ...
... impulse up to any part of its whole time , so that , if I be a constant depending on the masses and conditions of constraint involved , and if U , v , V denote the com- ponent velocities of the point struck , in the direction of the impulse ...
Page 284
... impulses , applied to a rigid body , or to a system of material points or rigid bodies con- nected in any way , is to be found most readily by the aid of D'Alembert's principle ; according to which the given impulses , and the impulsive ...
... impulses , applied to a rigid body , or to a system of material points or rigid bodies con- nected in any way , is to be found most readily by the aid of D'Alembert's principle ; according to which the given impulses , and the impulsive ...
Page 285
... impulse fulfils a maximum - tended by minimum condition . Lagrange extended this proposition to a system of bodies connected by any invariable kinematic re- Equation of lations , and struck with any impulses . Delaunay found that motion ...
... impulse fulfils a maximum - tended by minimum condition . Lagrange extended this proposition to a system of bodies connected by any invariable kinematic re- Equation of lations , and struck with any impulses . Delaunay found that motion ...
Page 286
... impulse P1 , Q1 , R1 , P2 , etc. does not vanish ( because ¿ 1 + u1 , ÿ , + v1 , etc. fulfil the prescribed velocity conditions ) . Hence every product Pu ,, Q , etc. vanishes . Hence now instead of ( g ) and ( h ) we have and Σ ( xu + ...
... impulse P1 , Q1 , R1 , P2 , etc. does not vanish ( because ¿ 1 + u1 , ÿ , + v1 , etc. fulfil the prescribed velocity conditions ) . Hence every product Pu ,, Q , etc. vanishes . Hence now instead of ( g ) and ( h ) we have and Σ ( xu + ...
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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.