Motion under different kinds of force

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1. Left-click the red object and drag a velocity (red) vector out from it. If unsuccessful, press "Reset" and try again.

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2. Left-click the red object again and drag an acceleration (blue) vector out from it.

3. When the red object is not moving, the two vectors can be modified by left-dragging their heads.

4. Translate the whole system by right-dragging (or control-dragging) the red object.

5. After the velocity and acceleration are created, select the force that acts on the red object.

6. When the "central force" is selected, a gray dot will appear. This is the centre of the central force. You can drag the gray dot to a new position.

7. To refresh the black dots on the locus, uncleck "Show locus" and check it again.

Bertrand's theorem:

Reference

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980), 2nd ed.

Lowell S. Brown Am. J. Phys. 46, 930 (1978)

Y. Tikochinsky, Am. J. Phys. 56, 1073 (1988)