Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xvi
... Path · SECTIONS 344-345xxvili . General investigation of Disturbed Path - Differential Equa- tion of Disturbed Path of Single Particle in a Plane - Ki- netic Foci - Theorem of Minimum Action - Action never a Minimum in a course ...
... Path · SECTIONS 344-345xxvili . General investigation of Disturbed Path - Differential Equa- tion of Disturbed Path of Single Particle in a Plane - Ki- netic Foci - Theorem of Minimum Action - Action never a Minimum in a course ...
Page 2
... path , if the path be a curve , or the path itself if a straight line . ( according 5. If the path be not straight the direction of motion changes from point to point , and the rate of this change , per unit of length of the curve ...
... path , if the path be a curve , or the path itself if a straight line . ( according 5. If the path be not straight the direction of motion changes from point to point , and the rate of this change , per unit of length of the curve ...
Page 3
... path described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent variable understood in the ...
... path described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent variable understood in the ...
Page 9
... path being always at the infinitely small distancer from the fixed straight 1 line , the axis of the cylinder ) , will have finite curvature The tortuosity , being tan a or 1 P 1 √pr ρ :( ( 1-9 ) will in the limit be a mean ...
... path being always at the infinitely small distancer from the fixed straight 1 line , the axis of the cylinder ) , will have finite curvature The tortuosity , being tan a or 1 P 1 √pr ρ :( ( 1-9 ) will in the limit be a mean ...
Page 17
... path , or the velocity is zero ; for [ § 9 ( 14 ) ] we have 2 2 2 8 ( d3 ) ' = ( d ' x ' ) ' + ( d'x ) 2 + ( de ) * − 2 1 ds2 - • dt2 dt dt dt P The direction cosines of the tangent to the path at any point x , y , z are 1 dx v dt ' 1 ...
... path , or the velocity is zero ; for [ § 9 ( 14 ) ] we have 2 2 2 8 ( d3 ) ' = ( d ' x ' ) ' + ( d'x ) 2 + ( de ) * − 2 1 ds2 - • dt2 dt dt dt P The direction cosines of the tangent to the path at any point x , y , z are 1 dx v dt ' 1 ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder degrees of freedom denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz dynamical ellipsoid equal equations of motion equilibrium expression finite fluid force formula function give given gyrostatic Hence impulse infinitely small instant integral kinetic energy length linear mass measured momentum moving negative notation osculating plane P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic motions solution space spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole zero αξ
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.