Lessons on Rigid Dynamics |
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Page 3
... inclined axis while carried forwards by the machine , and hundreds of other familiar cases , supply examples of translation combined with rotation . Examples of combined rotations are seen in the screw or paddles of a steamer , which ...
... inclined axis while carried forwards by the machine , and hundreds of other familiar cases , supply examples of translation combined with rotation . Examples of combined rotations are seen in the screw or paddles of a steamer , which ...
Page 12
... inclined to one another . The motions of points are no longer in one plane or in parallel planes . It will be neces- sary to represent the axes themselves . The way in which . an angular velocity is geometrically represented is as ...
... inclined to one another . The motions of points are no longer in one plane or in parallel planes . It will be neces- sary to represent the axes themselves . The way in which . an angular velocity is geometrically represented is as ...
Page 13
... The body is therefore rotating about OC . To settle its angular velocity about OC ; draw a perpen- Q A B C dicular to the plane AOB through O , and on this take a point Q. The angular velocities of the body round OA , OB INCLINED AXES . 13.
... The body is therefore rotating about OC . To settle its angular velocity about OC ; draw a perpen- Q A B C dicular to the plane AOB through O , and on this take a point Q. The angular velocities of the body round OA , OB INCLINED AXES . 13.
Page 14
... inclined to the former at an angle a . There will be a parallelopiped of angular velocities ; and in general the analogy between angular velocities and forces in Statics is complete . We will take for the illustration of this the ...
... inclined to the former at an angle a . There will be a parallelopiped of angular velocities ; and in general the analogy between angular velocities and forces in Statics is complete . We will take for the illustration of this the ...
Page 17
... inclined at an angle a . By the parallelogram of angular velocities the resultant axis is OR - between OC and OV — inclined to OC at an angle given by = sin ROC Ω sin ( a- ROC ) W Hence the motion is the same as if an imaginary right ...
... inclined at an angle a . By the parallelogram of angular velocities the resultant axis is OR - between OC and OV — inclined to OC at an angle given by = sin ROC Ω sin ( a- ROC ) W Hence the motion is the same as if an imaginary right ...
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Common terms and phrases
angular acceleration angular momentum angular velocity Cambridge centre of inertia centre of mass Christ's College cloth co-ordinates cos² couple Crown 8vo cylinder direction distance dt dt dt² effective forces ellipsoid English equal equilibrium Extra fcap fixed axis fixed point force acting friction geometrical Hence hoop horizontal plane impressed forces impulsive inclined kinetic energy late Fellow length 2a linear Mathematical middle point moment of inertia moments of inertia motion moving numerous oscillation Owens College particle pendulum perpendicular position pressure principal axes principle problem product of inertia Professor Prove radius radius of gyration resultant reversed right angles rigid body rotation round Schools Second Edition shew solution sphere straight line string suppose taking moments tion translation tube uniform rod vertical plane whence whole zero Σδη
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