| Motion in a non-inertial frame: |
mdv/dt = -¶U/¶r - mdV/dt + mr ´ dW/dt - 2mW ´ v - mW ´ (W ´ r) |
| Lagrange’s equations: |
 , ,
 |
| Hamilton’s equations: |
 ,
 ,
 |
| Lagrange multipliers: |
 ,
 |
| Small oscillations: |
 ,
 ,
 |
| Motion in a central potential: |
   ,
 Kepler orbit:  |
| Two interacting particles: | CM frame:
 |
| Relativistic kinematics: |
 |
| 4-vectors: |
 ,
  |
| Transformation of velocities: | u'|| = (u|| - v)/(1 - v×u/c2), u'^ = u^/(g(1 - v×u/c2)) |
| Doppler shift: | w' = gw(1 - (v/c)cosq) |
| Relativistic collisions: | For each
component pm of the 4-vector (p0,p1,p2,p3)
we have .
For transformations between reference frames we have  . |