Kinematics - Galilean Transform

Assuming the relative motion 'v' is along the x dimension then x -> x0 + vxt

or if we have components of velocity in all dimensions the transform will be:

t'
x'
y'
z'
=
1 0 0 0
vx 1 0 0
vy 0 1 0
vz 0 0 1
t
x
y
z

where:

in other words point:

t
x
y
z
is transformed to:
t
x + vxt
y + vyt
z + vzt

The nature of this transform is a shear (also known as skew) transform:

velocity transform before —» velocity transform after

When doing this we choose to make time 'absolute' in that the time lines are left horizontal wheras the position lines are skewed althogh I guess that this is just a covention and we could have skewed the time and made the distance absolute.

Shear (skew) Transform Matrix

The shear transform has the following characteristics:

for example the two dimensional matrix

a b
c d

we have:

a+d=2

ad-bc=1

 


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