Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page 1
... becomes zero at the angle . It is useful to consider at the outset various theorems connected VOL . I. 1 point . Motion of a with the geometrical notion of -PRELIMINARY -KINEMATICS SECTIONS Objects of the Chapter 1, Motion of a Point 3,
... becomes zero at the angle . It is useful to consider at the outset various theorems connected VOL . I. 1 point . Motion of a with the geometrical notion of -PRELIMINARY -KINEMATICS SECTIONS Objects of the Chapter 1, Motion of a Point 3,
Page 6
... become the direction cosines of the normal , PC , drawn towards the centre of curvature , C ; and λ , μ , v those of ... becomes 1 - P √ { ( d3x ) 2 + ( d3y ) 2 + ( d3z ) 2 — ( d3s ) " } ds1 ........... . ( 14 ) . Another formula for is ...
... become the direction cosines of the normal , PC , drawn towards the centre of curvature , C ; and λ , μ , v those of ... becomes 1 - P √ { ( d3x ) 2 + ( d3y ) 2 + ( d3z ) 2 — ( d3s ) " } ds1 ........... . ( 14 ) . Another formula for is ...
Page 13
... become more and more nearly equal , and in the limit , each is equal to the velocity at time t . Hence ds 2 = dt ' of velocity . 25. The preceding definition of velocity is equally applica- Resolution ble whether the point move in a ...
... become more and more nearly equal , and in the limit , each is equal to the velocity at time t . Hence ds 2 = dt ' of velocity . 25. The preceding definition of velocity is equally applica- Resolution ble whether the point move in a ...
Page 34
... the relative position and motion of the pursuer with regard to the pursued , we must impress on both a velocity equal and opposite to that of the latter , we see motion . at once that the problem becomes the same 34 [ 46 . PRELIMINARY .
... the relative position and motion of the pursuer with regard to the pursued , we must impress on both a velocity equal and opposite to that of the latter , we see motion . at once that the problem becomes the same 34 [ 46 . PRELIMINARY .
Page 35
... becomes the same as the following . A Relative boat crossing a stream is impelled by the oars with uniform velocity relatively to the water , and always towards a fixed point in the opposite bank ; but it is also carried down stream at ...
... becomes the same as the following . A Relative boat crossing a stream is impelled by the oars with uniform velocity relatively to the water , and always towards a fixed point in the opposite bank ; but it is also carried down stream at ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quantity radius ratio rectangular right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane theorem tion twist values whole x₁ y₁ αξ λ² аф