Rectilinear vs Curvilinear Motion: Explained

[SpaceExplorer]

If an object O is performing rectilinear motion w.r.t a Galilian body of reference K then w.r.t an accelerated body of reference K', O performs 'curvilinear' motion... What I ask for is a detailed explanation of this statement.

 

[proculation]

I don't have a detailed explanation but instinctively, I would say that since the spacetime is contracting, the body passing by the other body as no place to go but to go before you. In that case, that body accelerating cannot do anything but to curve light and from your point of view, it's a "curvilinear' motion.

 

[Ich]

What part of the statement are you having problems with?
body of reference (=reference frame)?
Galilean reference frame?
rectilinear motion?

For example, if you have a trajectory x=vt, y=0 in an inertial reference frame, how would it look in the frame t'=t, x'=x, y'=y-a/2*t² (which is an accelerated frame in pre-relativistic mechanics)?

 

[MikeLizzi]

Hope you don’t mind if I put the question in my own words first.

Given:
Three people start out together. Person ‘B’ is traveling at constant velocity in the x-direction with respect to Person ‘A’. Person ‘C’ is accelerating in the y-direction with respect to Person ‘A’.

Question:
What will the motion of Person ‘C’ be with respect to Person ‘B’?

Answer:
A curve in the x-y plane. (as you probably already suspect)

 

[SpaceExplorer]

Thanks 'Mikelizzi', for your reply which changed my interpretation of the statement... My prev's interp'n was that the body 'C' is accelerating in the same dir'n as is the motion of body 'B' w.r.t A... So for my 1st interpretation, would the movement of C would still look Curvilinear to B, or will it be rectilinear?

 

[DrGreg]

Draw a spacetime diagram, i.e. a graph of distance against time. If you have a straight-line graph relative to an inertial frame, you'll have a curved graph relative to an accelerating frame.