Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page x
... Tangent - Surface on Surface - Both traces prescribed ; one degree of freedom Twist - Estimation of Integral Twist in a Plane Curve ; in a Curve consisting of plane portions in different Planes ; in a continuously Tortuous Curve ...
... Tangent - Surface on Surface - Both traces prescribed ; one degree of freedom Twist - Estimation of Integral Twist in a Plane Curve ; in a Curve consisting of plane portions in different Planes ; in a continuously Tortuous Curve ...
Page 2
... tangent drawn to its path , if the path be a curve , or the path itself if a straight line . ( according 5. If the ... tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
... tangent drawn to its path , if the path be a curve , or the path itself if a straight line . ( according 5. If the ... tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
Page 3
... tangent , at any point x , y , to OX . Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with 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 + ...
... tangent , at any point x , y , to OX . Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with 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 + ...
Page 4
... tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning about the tangent to the curve . The tortuosity is therefore ...
... tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning about the tangent to the curve . The tortuosity is therefore ...
Page 5
... tangents to a curve at points separated by an arc of length ds . We have 80 2 sin 80 sin 80 1 = δε P 88 when ds is infinitely small ; and in the same limit . ( 7 ) dx 1 = m = ds dy ds ' dz n == ; ds dx dy dz a ' - a = d b ' b = d c'c d ...
... tangents to a curve at points separated by an arc of length ds . We have 80 2 sin 80 sin 80 1 = δε P 88 when ds is infinitely small ; and in the same limit . ( 7 ) dx 1 = m = ds dy ds ' dz n == ; ds dx dy dz a ' - a = d b ' b = d c'c d ...
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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.