Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xv
... Equal Roots - Case of Equal Roots and Evanescent Minors - Routh's Theorem - Case of no Motional Forces - Conservative Positional , and no Mo- tional , Forces - Equation of Energy in Realized General Solution · SECTIONS 338 339-341 .342 ...
... Equal Roots - Case of Equal Roots and Evanescent Minors - Routh's Theorem - Case of no Motional Forces - Conservative Positional , and no Mo- tional , Forces - Equation of Energy in Realized General Solution · SECTIONS 338 339-341 .342 ...
Page xvi
... equal two and two - Orthogonalities proved between two components of one fundamental oscillation ; and equality of their Energies - Orthogonalities proved be- tween different fundamental oscillations - Case of Equal Periods Completed ...
... equal two and two - Orthogonalities proved between two components of one fundamental oscillation ; and equality of their Energies - Orthogonalities proved be- tween different fundamental oscillations - Case of Equal Periods Completed ...
Page xvii
... equal - If two sides , deviating infinitely little from the third , are together equal to it , they con- stitute an unbroken natural course - Natural course proved not a course of Minimum Action , beyond a Kinetic Focus -A course which ...
... equal - If two sides , deviating infinitely little from the third , are together equal to it , they con- stitute an unbroken natural course - Natural course proved not a course of Minimum Action , beyond a Kinetic Focus -A course which ...
Page 16
... equal increments in equal times , and is then measured by the actual increase of velocity per unit of time . If we choose as the unit of acceleration that which adds a unit of velocity per unit of time to the velocity of a point , an ...
... equal increments in equal times , and is then measured by the actual increase of velocity per unit of time . If we choose as the unit of acceleration that which adds a unit of velocity per unit of time to the velocity of a point , an ...
Page 18
... equal to the acceleration of the velocity — the other towards the centre of curvature ( perpendicular therefore to the direction of motion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of ...
... equal to the acceleration of the velocity — the other towards the centre of curvature ( perpendicular therefore to the direction of motion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of ...
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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.