Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 10
... equation is lx + my + nz = P , touches the ellipsoid at x ' , y ' , ' , this equation must be iden- tical with a2 1 + yy b2 y ' = 1 ; c2 -22 1000 • . 1 = 2 = - 2 b2 ( ) ' + ( ) 2 + ( ) .. moment required = M 5 m 2 = c2 = n p • a2 l2 + ...
... equation is lx + my + nz = P , touches the ellipsoid at x ' , y ' , ' , this equation must be iden- tical with a2 1 + yy b2 y ' = 1 ; c2 -22 1000 • . 1 = 2 = - 2 b2 ( ) ' + ( ) 2 + ( ) .. moment required = M 5 m 2 = c2 = n p • a2 l2 + ...
Page 15
... equations arising from horizontal and vertical re- solution , the last from taking moments about an axis through C perpendicular to plane OAB ; .. O 2 F. AC + Mw.AC. CO + Mg . Co , = 0 = 2 F ' . AC + Mw2 . AC . CO - Mg . CO . These ...
... equations arising from horizontal and vertical re- solution , the last from taking moments about an axis through C perpendicular to plane OAB ; .. O 2 F. AC + Mw.AC. CO + Mg . Co , = 0 = 2 F ' . AC + Mw2 . AC . CO - Mg . CO . These ...
Page 20
... equation of motion of the body is d2 & a2 2 dt2 φ 2 α g cos p , . . § à2 ( dd ) 2 = C + √√2 . ag cos p . dt The limit of w will result from making аф = dt 0 , when ゆ= I π 2 .. aw2 = 2√2.8 , and in this case the 20 MOTION OF A BODY.
... equation of motion of the body is d2 & a2 2 dt2 φ 2 α g cos p , . . § à2 ( dd ) 2 = C + √√2 . ag cos p . dt The limit of w will result from making аф = dt 0 , when ゆ= I π 2 .. aw2 = 2√2.8 , and in this case the 20 MOTION OF A BODY.
Page 25
... equation of moments about A and B in succession , we have a R = Σ { mr ( a− r ) } w , aR ' = Σ ( mr2 ) w , Ꭱ aΣ ( mr ) – Σ ( mr2 ) R ' Σ ( mr2 ) = = 1 . -- 100 1/18 This solution and result will apply as well if the position of the ...
... equation of moments about A and B in succession , we have a R = Σ { mr ( a− r ) } w , aR ' = Σ ( mr2 ) w , Ꭱ aΣ ( mr ) – Σ ( mr2 ) R ' Σ ( mr2 ) = = 1 . -- 100 1/18 This solution and result will apply as well if the position of the ...
Page 27
... equation of its motion after the blow will be ďo dt2 ( a2 + k2 ) = - ga sin o , being measured from the original distance of the rod . αφ .. ( a2 + 10 ° 2 ) ( dp ) 2 = C + 2ga cos p . Now by the conditions of the question ( a2 + k2 ) w2 ...
... equation of its motion after the blow will be ďo dt2 ( a2 + k2 ) = - ga sin o , being measured from the original distance of the rod . αφ .. ( a2 + 10 ° 2 ) ( dp ) 2 = C + 2ga cos p . Now by the conditions of the question ( a2 + k2 ) w2 ...
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2g h accelerating force Algebra angle angular velocity ball blow c² a² CA² Calculus Cambridge centre of gravity co-ordinate axes cone Conic Sections cos² cube cylinder diameter Differential Differential Calculus direction cosines disc distance dt dt dt dy dx dt dy dt effective force Examples Geometry Hence horizontal action horizontal and vertical HYMERS DR impulse inertia instantaneous axis invariable plane length Let C fig Ma² mass Mk² moment of inertia moves Mr² oscillation P₁ P₂ parallel particle perpendicular plates point of contact position pressure principal axes principle R₁ radius reaction revolves rotation sin² sphere tan² Third Edition Treatise velocities of translation vis viva w₁ w₂ wheel WHEWELL DR аф ᏧᎾ
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