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Pb. 9.24 Find the approximate form of the above expression for u when
β << 1, and show that it reduces to the expression of velocity addition in
Newtonian mechanics.

In-Class Exercises
π c
Pb. 9.25 Find the angle θ, if ′ =θ and u ′ = v = .
2 2
Pb. 9.26 Plot the angle θ as a function of θ′ when v/c = 0.99 and u′/c = 1.

Pb. 9.27 Let the variable φ be defined such that tanh(φ) = β. Write the
Lorentz transformation matrix as function of φ. Can you give the Lorentz
transformation a geometric interpretation in non-Euclidean geometry?
Pb. 9.28 Using the result of Pb. 9.27, write the resultant transformation from
a boost with parameter φ , followed by another boost with parameter φ . Does
1
2
this rule for composition of Lorentz transformations remind you of a similar
transformation that you studied previously in this chapter?

9.5 MATLAB Commands Review

colormap Control the color mix of an image.
fliplr Flip a matrix left to right.
flipud Flip a matrix in the up-to-down direction.
imagesc Create a pixel intensity map from data stored in a matrix.
load Import data files from outside MATLAB.
rot90 Rotate a matrix by 90°.
toeplitz Specialized matrix constructor that describes, inter alia,
the operation of a blur in an image.

© 2001 by CRC Press LLC