Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Results 1-5 of 61
Page 2
... circle , and radii to the points of contact . The angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be ...
... circle , and radii to the points of contact . The angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be ...
Page 20
... circle . Let a be the velocity , and a the angle through which its direc- tion turns in unit of time ; then , by properly choosing the axes , we have whence dx dt == a sin at , dy dt = a cos at , ( x − A ) ' + ( y — B ) 2 = a . " . b ...
... circle . Let a be the velocity , and a the angle through which its direc- tion turns in unit of time ; then , by properly choosing the axes , we have whence dx dt == a sin at , dy dt = a cos at , ( x − A ) ' + ( y — B ) 2 = a . " . b ...
Page 22
... circle of radius r with uniform angular velocity ( about the centre ) , and let this circle move perpen- dicular to its plane with velocity V. The point describes a helix on a cylinder of radius r , and the inclination a is given by ...
... circle of radius r with uniform angular velocity ( about the centre ) , and let this circle move perpen- dicular to its plane with velocity V. The point describes a helix on a cylinder of radius r , and the inclination a is given by ...
Page 26
... circle , whatever be the form and dimensions of the orbit . In the motion of a planet or comet , the acceleration is directed towards the sun's centre . Hence ( § 36 , b ) the velocity is in- duced from Kepler's laws . of planet or ...
... circle , whatever be the form and dimensions of the orbit . In the motion of a planet or comet , the acceleration is directed towards the sun's centre . Hence ( § 36 , b ) the velocity is in- duced from Kepler's laws . of planet or ...
Page 27
... circle whose diameter is the major axis , if the orbit be an ellipse or hyper- bola ; in the tangent at the vertex if a parabola . parabola . Measure off on the perpendicular a third proportional to its own length and any constant line ...
... circle whose diameter is the major axis , if the orbit be an ellipse or hyper- bola ; in the tangent at the vertex if a parabola . parabola . Measure off on the perpendicular a third proportional to its own length and any constant line ...
Contents
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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.