mech_5_rigid_body_kinetics

mech_5_rigid_body_kinetics - Centre of Mass Centre of mass...

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Centre of Mass Centre of mass definition. m i r i = M r G (1) M - total mass r G - centre of mass position From diagram, r i = r G + ρ i therefore m i r i = m i (r G + i ) = m i r G + m i i = M r G + m i i Since (1), therefore m i i = 0 (2) From (1), we can deduce m i = M and m & r i & r G i && rM r iG = From (2), we can deduce m i & i = 0 and m i i = 0 1
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Triple Scalar Product Consider 3 vector A , B , C , . A , B on x-y plane C on y-z plane A x B = | A | | B | sin α k | A | | B | sin is the area of the parallelogram abcd. Therefore A x B C = | A | | B | sin k C = ( | A | | B | sin ) (| C | cos β ) By symmetry, the volume can be written as :- A x B C = B x C A = C x A B Since dot product is commutative, the vol. is C A x B = A B x C = B C x A i.e. Position of dot and cross operator is interchangeable therefore A x B C = A B x C = AAA BBB CCC xy z z z The sign of the result is unaltered provided that the cyclic order is preserved. Reverse order will introduce a change of sign.
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This note was uploaded on 05/10/2009 for the course MXXM 2XX9 taught by Professor Gxxy during the Spring '09 term at City University of Hong Kong.

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mech_5_rigid_body_kinetics - Centre of Mass Centre of mass...

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