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Decomposing Motions

  1. May 15, 2010 #1
    Can anybody help me to solve this question?

    Consider the motion T:R(4) to R(4) given by T(x,y,z,w)=(w+3,x,y,z+1) T as a composition of traslations, reflections and rotations.
     
  2. jcsd
  3. May 15, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi gezmisoguz! Welcome to PF! :smile:
    Well, the obvious thing to do is to go via (w,x,y,z) :wink:
     
  4. May 15, 2010 #3
    Re: Welcome to PF!

    Thanks:)

    I tried to use that but i can not reach translation rotation and reflection form of this.

    Please give some hints to me:)
     
  5. May 15, 2010 #4

    HallsofIvy

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    First step T(x,y,z,w)= (w, x, y, z)+ (3, 0, 0, 1). That (3, 0, 0, 1) is a translation.

    Now, what is U(x,y,z,w)= (w, x, y, z)?
     
  6. May 15, 2010 #5
    We must use a matrix to change basis of (w,x,y,z). Can this matrix contain rotation and reflection?
     
  7. May 16, 2010 #6
    Couldn't you have thought of a better title?
     
  8. May 17, 2010 #7

    HallsofIvy

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    Well, what have you done on this? Have you written it as a matrix? What is the determinant of that matrix?
     
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