Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Results 1-5 of 54
Page 2
... suppose two tangents drawn to a 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 ...
... suppose two tangents drawn to a 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 ...
Page 7
... Suppose a line , drawn from a fixed point , to move so as always to be parallel to the direction of motion of a point describing the curve : the angle through which this turns during the motion of the point exhibits what we have thus ...
... Suppose a line , drawn from a fixed point , to move so as always to be parallel to the direction of motion of a point describing the curve : the angle through which this turns during the motion of the point exhibits what we have thus ...
Page 23
... ( suppose ) , μ 2 y == y dx2 This gives , if μ is negative , y = P c COS ( + Q ) , the harmonic curve , or curve of sines . 20 28 лв If μ be positive , y = Pe3 + Q € ̃3 ; and by shifting the origin along the axis of x this can be put in ...
... ( suppose ) , μ 2 y == y dx2 This gives , if μ is negative , y = P c COS ( + Q ) , the harmonic curve , or curve of sines . 20 28 лв If μ be positive , y = Pe3 + Q € ̃3 ; and by shifting the origin along the axis of x this can be put in ...
Page 24
... ( suppose ) . dt dt In polar co - ordinates this is do h = p2 dt = 2 dA dt if A be the area intercepted by the curve , a fixed radius - vector , and the radius - vector of the moving point . Hence the area in- creases uniformly with the ...
... ( suppose ) . dt dt In polar co - ordinates this is do h = p2 dt = 2 dA dt if A be the area intercepted by the curve , a fixed radius - vector , and the radius - vector of the moving point . Hence the area in- creases uniformly with the ...
Page 30
... Suppose Ox to be the line of motion of the first point , whose velocity is v , AP the curve of pursuit , in which the velocity is u , then the tangent at P always passes through Q , the instan- taneous position of the first point . It ...
... Suppose Ox to be the line of motion of the first point , whose velocity is v , AP the curve of pursuit , in which the velocity is u , then the tangent at P always passes through Q , the instan- taneous position of the first point . It ...
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.