Hello Group...
I am new to the group and this is my first post.
I am looking for some help in the application of length contraction and time dilation calculations. All of the text books that I have referenced show examples where an observer is translating at zero or ninety degrees relative to the other frame of reference. I would like to calculate the effects when the frames are moving at say 45 or 135 degrees to one another.
I would appreciate any direction in this regard.
Sincerely,
Tom Miles

Treat it as a vector quantity.

An object directly toward or away from the observer is subject to the full "beta" contraction (or time dilation) while for one moving at right angles, there is none ("beta"= 1). For an object moving at angle theta, it would be beta*sin(theta)+ 1*cos(theta).

Thank you, Hallsofivy...
I will start working on your approach to see what I get.
Attached are some diagrams and calculations in a .pdf file relating to the problem. The calculations are straight out of Resnick's "Introduction to Special Relativity."
In looking at Diagram D, it appears to be a combination of both Length Contraction and Time Dilation. Perhaps that is what will be revealed when I follow your methodology.
Again, thank you for your input.
Sincerely,
Tom Miles

.PDF file is attached.