1. Fictitious Force

2. Inertial Lagrangian  The Lagrangian is defined in an inertial system. Follows Newton’s lawsFollows Newton’s laws Equivalent in other inertial systemsEquivalent in other inertial systems  Hamilton’s equations are similarly unaffected by a change to another inertial system.

3. Accelerating Coordinates  Select Cartesian coordinates with acceleration. Transform along that coordinate  The kinetic energy will be changed. x1’x1’ x2x2 x1x1 x2’x2’ a

4. No External Force  Let the accelerated system have no external force. Zero potentialZero potential  The Euler-Lagrange equations have a force-like term. Apparent potentialApparent potential  This is a fictitious force. Only the accelerated frameOnly the accelerated frame

5. Rotating Coordinates  A rotating coordinate system is non-inertial. Time-dependent angle Transform coordinates Transform velocities x2x2 x2’x2’ x1x1 x1’x1’ tt

6. Rotating Motion  Rewrite the kinetic energy in terms of the rotating coordinates. Summation rule usedSummation rule used  Find the three EL equations.

7. Wedge Products  The extra terms can be expressed as a vector product.  Define the angular velocity  along 3-axis. Product terms only for 1- and 2-axesProduct terms only for 1- and 2-axes

8. Vector Form  The vector products can be used to create a vector equation.  In the rotating frame there are two fictitious forces unrelated to the potential. Centrifugal force Coriolis force next