The definitions Lucy Venable cited on April 23 are very useful. I agree that "axial movement" is probably not the best term for the indication shown in Ex. a) below. Perhaps just saying "movement in place" is better.
I think Lucy's method of indicating moving in place, as in Ex. b), is a good idea for certain situations. However, I believe Ex. a) and Ex. b) make slightly different statements.
As I see it, Ex. b) is more specific. It says do three movements of equal duration in place; the last movement is continued freely at a relatively moderate tempo. In contrast, Ex. a) only says "move in place"; no other aspects of the movement are stated.
Perhaps my interpretation of Ex. a) would be clearer if I compare it with the sign for meandering, which is shown in Ex. c). As I understand it, the sign for meandering simply says "go from one place to another." Nothing else is indicated. The type(s), number, path(s) and timing of the movements used to travel is (are) irrelevant. The focus is not on the movements or paths; rather it is on idea of going from one place to another.
The opposite of meandering is moving in place. Here too the type(s), number and timing of the movements that one does in place is (are) irrelevant. The focus is just on moving in place.
Perhaps the opposite of meandering could be indicated with a meandering sign that has a slash through it, as in Ex. d). However, that indication seems to make a negative statement: "don't meander, don't go from one place to another." Ex. a) has a similar meaning, except it makes the positive statement, "move in place.