Results 1 to 6 of 6

Math Help - shear

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    49

    shear

    Hey everyone... can some one explain to me why a vertical shear of 5 is NOT
    1 0
    0 5

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jul 2009
    Posts
    6
    Well the general form for a vertical shear is

    1 0
    m 1

    but you can also tell by multiplying it by the basis vectors.

    [[1,0],[0,5]]*[1,0]=[1,0]

    so you see the (1,0) vector does not change in the transformation, which should not be the case in a vertical shear. What this actually does is stretch everything out, because as you can see any y value is multiplied by 5, where in a shear transformation the magnitude of the y value changes according to the x value.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    49
    ok so for a vertical shear, u put the variable in the 'x' column...??
    so it should be
    1 0
    5 1 ??

    i dont quite understand why the 5 isnt in the y column
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2009
    Posts
    6
    Thats correct.

    think about how something in a vertical sheer moves. It moves vertically, but the magnatitude of that movement is determined by its horizontal position (the farther it's x value is from zero the more its y value changes)

    so [[1,0],[5,1]]*[x,y] = [x,(5*x+y)]

    so while you could say 5 is in the 'x collumn', because it is multiplied by x, it is in the 'y row', because that product is added to y*1 to become the new y value.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2009
    Posts
    49
    ok so if you have a point on the x, y plane, say (2, -1)... in matrix form it would be written as [2 -1]


    then how come in my book under matrix transformation it has it written as
    [2
    -1]

    ??
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2009
    Posts
    6
    In matrix form they should be put one on top of the other, but that can be hard to type on a computer so to make a matrix sometimes people will use brackets inside brackets (like how x^2 means x squared)

    so [[1,2],[3,4]] would be similar to

    1 2
    3 4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Shear and transformation matrix
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: May 9th 2011, 04:44 AM
  2. Shear transformation problem
    Posted in the Geometry Forum
    Replies: 6
    Last Post: March 27th 2011, 07:48 AM
  3. Shear Stress
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: May 7th 2010, 02:10 AM
  4. Shear Flow
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: September 22nd 2009, 07:23 PM
  5. shear stress calculation help
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 16th 2009, 05:59 AM

Search Tags


/mathhelpforum @mathhelpforum