Treatise on Natural Philosophy, Volume 1, Issue 1At the University Press, 1879 - Mechanics, Analytic |
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Page 3
... reference to any independent variable t , we have do Also , = ( dy d dx 1 + dy dx d'y - dy d3x dx2 + dy2 dx ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius of curvature , so that 1 do Ρ ds 1 we conclude Ρ dx d'y - dy d2x ( dx2 + ...
... reference to any independent variable t , we have do Also , = ( dy d dx 1 + dy dx d'y - dy d3x dx2 + dy2 dx ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius of curvature , so that 1 do Ρ ds 1 we conclude Ρ dx d'y - dy d2x ( dx2 + ...
Page 10
... reference to the other , is called the Evolute . 18. It will be observed that we speak of an involute , and of the evolute , of a curve . In fact , as will be easily seen , a curve can have but one evolute , but it has an infinite ...
... reference to the other , is called the Evolute . 18. It will be observed that we speak of an involute , and of the evolute , of a curve . In fact , as will be easily seen , a curve can have but one evolute , but it has an infinite ...
Page 37
... reference to a second point B ; if B executes any other motion with refer- ence to a third point C ; and so on - the first is said to execute , with reference to the last , a movement which is the resultant of these several movements ...
... reference to a second point B ; if B executes any other motion with refer- ence to a third point C ; and so on - the first is said to execute , with reference to the last , a movement which is the resultant of these several movements ...
Page 38
... position or the middle of its range . Epoch in angular measure is the angle described on the circle of reference in the period of time defined as the epoch . harmonic The Period of a simple harmonic motion is the 38 [ 52 . PRELIMINARY .
... position or the middle of its range . Epoch in angular measure is the angle described on the circle of reference in the period of time defined as the epoch . harmonic The Period of a simple harmonic motion is the 38 [ 52 . PRELIMINARY .
Page 86
... and instantaneous axis . joyed by a Two co - ordinates , A'OB , and measured in a plane per- pendicular to 40 , from a fixed plane of reference to the plane AOB , fully specify the position of the moveable body 86 [ 109 PRELIMINARY .
... and instantaneous axis . joyed by a Two co - ordinates , A'OB , and measured in a plane per- pendicular to 40 , from a fixed plane of reference to the plane AOB , fully specify the position of the moveable body 86 [ 109 PRELIMINARY .
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acceleration according action actual altered amount angle angular velocity application axes axis becomes body called Cambridge centre circle co-ordinates coefficients complete component condition configuration consider constant corresponding course curvature curve denote described determined differential direction displacement distance edition equal equations equilibrium Example expression finite fixed force function give given harmonic Hence inertia infinitely small instant integral kinetic energy length less mass matter mean measured motion moving natural negative observations parallel particle particular path period perpendicular plane position present principle problem produced proved quantity radius reference relative remain remarkable respectively resultant rigid rolling roots rotation round side simple solution space spherical strain suppose surface tangent theorem tion turn unit University values whole
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.