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by: Hyman Bailey

DiffEquationwithLinearAlg MAT2705

Marketplace > Villanova University > Mathematics (M) > MAT2705 > DiffEquationwithLinearAlg
Hyman Bailey
GPA 3.66


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Class Notes
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This 4 page Class Notes was uploaded by Hyman Bailey on Wednesday October 28, 2015. The Class Notes belongs to MAT2705 at Villanova University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/230555/mat2705-villanova-university in Mathematics (M) at Villanova University.


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Date Created: 10/28/15
Rotations iFirst we de ne the three generic rotation matrices all counterclockwise rotations about X y and z axes respectively gt restart l 0 0 gt A1 0 cosa sina 0 sina cosa l 0 0 14 0 cosa sina 1 0 sina cosa cosb 0 sinb gt 3 0 l 0 sinb 0 cosb cosb 0 sinb 3 0 l 0 2 sinb 0 cosb cosc sinc 0 gt C1 sinc cosc 0 0 0 l cosc sinc 0 C sinc cosc 0 3 0 0 l gt Example 1 first rotation about yaxis counter second about zaxis clockwise both by 45 degrees 7 11 1 1 1 2 2 J 2 1 1 1 2 rot 2 2 J 2 12 1 1 J 0 J 2 2 x gt V2 y z x v y 13 2 7gt E rotv 1 1 1 2 2 x 2 J y 2 z 1 l 1 E7 2x2J7y 22 14 1 1 3 x 3 J22 gt solveE1xE2yE32 xyz 7 x zzyzzz 15 so a vector along the aXis of rotation would be 1 5 gt v 1 1 1 5 1 1 16 a perpendicular vector to this aXis is 0 gt w l l 17 w 1 1 the rotated vector is gt rotw rotw 1 1 2 2 2 J 1 1 2 rotw 2 2 l 1 3 5 to find the angle between w and rotw we do gt withLinearAlgebra gt 9 VectorAnglew rotw 9 arccos 180 gt evalf5 v 7 62797 gt diagarrow000 111 005 1 rotbarrow000 010 05 1 1 rotcarrow000 001 05 1 1 rotcb arrow000 v1v2 v3 green 1 colorblue colorblue 2 1 optional to Visualize the angle of the combined rotation we can draw some vectors gt with plottools 1 17 18 19 110 colorb lue color plots display diagrotcbrotbrotcaxesboxed scaling constrained orientation 2070


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