Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page ix
... Resultant Motion 45-49 50 , 51 Harmonic Motion 52-57 Composition of Simple Harmonic Motions in one Line Mechanism for compounding , and Graphical Representation of , 58-61 Harmonic Motions in one Line 62 Composition of S. H. M. in ...
... Resultant Motion 45-49 50 , 51 Harmonic Motion 52-57 Composition of Simple Harmonic Motions in one Line Mechanism for compounding , and Graphical Representation of , 58-61 Harmonic Motions in one Line 62 Composition of S. H. M. in ...
Page xii
... Resultant round any point in that Plane - Any number of Moments in one Plane compounded by addition - Moment round an Axis - Moment of a whole Motion round an Axis - Re- sultant Axis · Virtual Velocity - Virtual Moment Work - Practical ...
... Resultant round any point in that Plane - Any number of Moments in one Plane compounded by addition - Moment round an Axis - Moment of a whole Motion round an Axis - Re- sultant Axis · Virtual Velocity - Virtual Moment Work - Practical ...
Page xvi
... Resultant Motion reduced to Motion of a Conservative System with four fundamental periods equal two and two - Orthogonalities proved between two components of one fundamental oscillation ; and equality of their Energies ...
... Resultant Motion reduced to Motion of a Conservative System with four fundamental periods equal two and two - Orthogonalities proved between two components of one fundamental oscillation ; and equality of their Energies ...
Page 15
... resultant velocity in magnitude and direction . A OC is evidently the diagonal of the parallelogram two of whose sides are ОА , ОВ . Hence the resultant of velocities represented by the sides of any closed polygon whatever , whether in ...
... resultant velocity in magnitude and direction . A OC is evidently the diagonal of the parallelogram two of whose sides are ОА , ОВ . Hence the resultant of velocities represented by the sides of any closed polygon whatever , whether in ...
Page 17
... resultant acceleration are 1 dx 1 d'y 1 d'z F dt ' F dt ' ƒ dť2 ' where , for brevity , we denote by f the resultant acceleration . Hence the direction cosines of the plane of these two lines are - dyd❜z - dzd3y { ( dyd3z — dzd3y ) 2 + ...
... resultant acceleration are 1 dx 1 d'y 1 d'z F dt ' F dt ' ƒ dť2 ' where , for brevity , we denote by f the resultant acceleration . Hence the direction cosines of the plane of these two lines are - dyd❜z - dzd3y { ( dyd3z — dzd3y ) 2 + ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative 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 simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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