Elements of Natural Philosophy, Volume 1 |
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Page 3
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
Page 15
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in VS produced , so that YS SU is constant , the locus of U is easily seen to be a circle ...
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in VS produced , so that YS SU is constant , the locus of U is easily seen to be a circle ...
Page 16
... turned through by its radius - vector in the same time , 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
... turned through by its radius - vector in the same time , 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
Page 17
... turned . Hence ( 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as ...
... turned . Hence ( 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as ...
Page 18
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem theory tion torsion uniform unit vertical whole wire