The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies: Being Lectures on Mathematical Physics |
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Common terms and phrases
A₁ acceleration accordingly angle angular momentum angular velocity arbitrary constants b₁ called center of mass centrifugal coefficients components cone consider const cos² curve cyclic d'Alembert's principle derivatives differential equation direction cosines displacement distance dt dt dx dy Dynamics ellipse ellipsoid equal equations of motion equilibrium force function geometrical given Green's theorem H₂ Hamilton's Principle harmonic horizontal inertia instantaneous axis kinetic energy Lagrange's equations linear moment of inertia momentum multiplied normal obtain oscillation P₁ parallel parameter particle path perpendicular plane point-function polhode position potential energy principle quadratic quadratic function quadric quantities rigid body rotation sin² 9 sphere Suppose surface integral tangent theorem vanish variable vertical vibration X₁ Y₁ zero Απ ат ди др ду дф дх
Popular passages
Page 21 - 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.
Page 22 - To every action there is always an equal and contrary reaction ; or the mutual actions of any two bodies are always equal and oppositely directed.
Page 468 - For compressible flow this becomes: where y is the ratio of the specific heat at constant pressure to that at constant volume...
Page 29 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 29 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 364 - The attraction of a uniform spherical surface on an external point is the same as if the whole mass were collected at the centre.
Page 28 - It appears from the table of dimensions, Art. 628, that the number of electrostatic units of electricity in one electromagnetic unit varies inversely as the magnitude of the unit of length, and directly as the magnitude of the unit of time which we adopt.
Page 367 - In planetary theory the adopted ratio of the mass of the Earth to the mass of the Moon is...
Page 22 - II Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis ilia imprimitur.
Page 66 - The quantity ^-mv2, ie half the product of the mass of a particle into the square of its velocity, is called the kinetic energy of the particle. Let us consider again a particle of constant mass m moving with a constant acceleration, and hence with a constant force ; let v be the velocity, s the space described at the time t; v', s' the corresponding values at the time t'.