Question

Please explain me what is Coordinate frames with Relative Translation Motion

Answer 1

A coordinate frame is a system by which the location of a point can be specified such as longitude and latitude or the X,Y and Z axes.
If I have say an X,Y and Z axes made out of say green K'Nex (kids toy, well maybe not just for kids ;) ) and I make another X1,Y1 and Z1 out of red K'nex and sit both of them ( at different ends,say) on the table ....then I have two coordinate frames either of which could be used to say where the centre of the table was.

If I move one of these (it doesn't matter which) and then if I imagine looking at the location of the origin of one (green say) with respect to (red) the other it will appear to be moving (or visa-versa).

Now imagine there's no table ... only green coordinate frame and red coordinate frame..
If i sit on the origin in red, to me, green looks to be moving. If I sit on the origin in green the red coordinate frame appears to be moving. I presume by translation it means straight line. (maybe "uniform translation motion" is meant ?)

So the green origin has translation motion as viewed from red and red has translation motion as viewed from green .....or.... the green and red coordinate frames have relative translation motion.


my 2 cents +/- 2 cent worth

Answer 2

Imagine you're in a car in a two-way street. You're driving at 60kmph The car from behind tries to overtake you. It is driving at 65 kmph. How do you see it happening? The car that is overtaking seems to pass by you really slow! It's as if, the car is travelling at 5 kmph. Now, another car in the OPPOSITE lane passes by you. It seems to whiz by, doesn't it? Well, that is because you're looking at objects sitting within your car (your REFERENCE FRAME).

The very idea of reference frame is to IMAGINE how you would view the motion of another object while you're sitting in another object. For example you're looking at a tree. For you the tree is stationary as both the tree and you are in the ground/earth frame. But, an astronaut shall find you both to be moving, since the earth (read: your refernce frame) itself is both rotating and revolving around the sun.

Answer 3

Mathematically it works like this. Suppose your reference frame is travelling at velocity v1i +v2j. Now, the idea is that ANYTHING that is not in your reference frame shall have velocity = -v1i-v1j+(the velocity of the other object). That is you need to subtract your VELOCITY (note- I'm not saying speed) from the velocity of the other object.

For example, the car that was overtaking you. Let the velocity of the car be v3i+v4j. <<This would be the velocity of the car as observed from the ground frame (that is: had you been standing on the ground)
But to you, in your car (your reference frame): it seems like (v3-v1)i+(v4-v2)j. It's easy to see that the magnitude of this is less than v3i+v4j vector. So, the 65kmph car seems to be travelling at 5 kmph. The direction can be calculated vectorically.

Similarly the car in the opposite lane has velocities say -v5i-v6j (negative, since the opposite lane). From your car it seems (-v5-v1)i+(-v6-v3)j... magnitude wise it increases (whizzing by), while the overall direction is negative to that of your's (since opposite lane ).

Now, vote me or give me my medal. I'm new, I need them.