Dynamics: Or a Treatise on Motion; to which is Added a Short Treatise on Attractions |
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Common terms and phrases
accelerating force altitude angular motion angular velocity apse apsidal ascend attraction centre of force centre of gravity centrifugal force circle co-ordinate axes consequently constant cos² curvature cycloid d₁ descend determine the motion differential direction distance elastic ellipse ellipsoid equal equations of motion fixed axis fixed point force acting given velocity Hence horizontal impact impressed forces impulsive inclined plane inertia with respect integral latus rectum loge m₁ mass moment of inertia Multiply orbit origin oscillation parallel particle path pendulum perpendicular position pressure principal axes PROB radius revolve rotation shew shewn sin² sphere string suppose surface tangent tension tion uniform vertical vis viva viva w₁ w₂
Popular passages
Page 368 - ... sphere attracted to a given centre of force varying as the distance is projected with a given velocity along a plane passing through that centre, friction being such as to destroy all sliding: prove that the path will be an ellipse, and find the velocity that the ellipse may be a circle. PROB. 28. A cone of given form, and supported at G its centre of gravity, has a motion communicated to it round an axis through G perpendicular to the line joining G with a point in the circumference of the base,...
Page 360 - If a body be projected about a centre of force varying inversely as the square of the distance with a velocity equal to n times the velocity in a circle at the same distance, and in a direction making an angle...
Page 359 - A body, projected in a given direction with a given velocity and attracted towards a given centre of force, • " has its velocity at every point: the velocity in a circle at the same distance :: 1...
Page 357 - ... (9.) A perfectly elastic ball falls from a height h, on a plane inclined 30 degrees to the horizon, shew that it will strike the plane again after an interval equal to twice the time of its fall, and that its range on the plane will be 4 h. (10.) A spherical particle of which...
Page 195 - Expressed in words, this equation states that the polar moment of inertia for an area, with respect to an axis perpendicular to its plane, is equal to the sum of the moments of inertia about any two mutually perpendicular axes in its plane that intersect on the polar axis.
Page 356 - A perfectly elastic ball descends down the chord AC, and being reflected by the plane BC, describes its path as a projectile ; show that the body will strike the circle at the opposite extremity of the diameter CD.
Page 260 - If two equal bodies, which attract each other with forces varying inversely as the square of the distance, are constrained to move in two straight lines at right angles to each other...
Page 360 - If a force vary inversely as the 7 th power of the distance, and a body be projected from an apse with a velocity which is to the velocity in a circle at the same distance :: 1 : \/3 ; find the polar equation to the curve described, and transform it to rectangular co-ordinates.
Page 358 - A body acted upon by two central forces, each varying inversely as the square of a distance, is projected from a point between them towards one of the centres: required the velocity of projection that the body may just arrive at the neutral point of attraction and remain at rest there.
Page 177 - The Vis Viva of a particle is the product of its mass into the square of its velocity. The principle of vis viva. If a system be in...