Download Presentation
## Fictitious Force

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**The Lagrangian is defined in an inertial system.**Follows Newton’s laws Equivalent in other inertial systems Hamilton’s equations are similarly unaffected by a change to another inertial system. Inertial Lagrangian**Accelerating Coordinates**• Select Cartesian coordinates with acceleration. • Transform along that coordinate • The kinetic energy will be changed. a x2 x2’ x1’ x1**Let the accelerated system have no external force.**Zero potential The Euler-Lagrange equations have a force-like term. Apparent potential This is a fictitious force. Only the accelerated frame No External Force**Rotating Coordinates**• A rotating coordinate system is non-inertial. • Time-dependent angle • Transform coordinates • Transform velocities x2’ x2 x1’ wt x1**Rewrite the kinetic energy in terms of the rotating**coordinates. Summation rule used Find the three EL equations. Rotating Motion**The extra terms can be expressed as a vector product.**Define the angular velocity w along 3-axis. Product terms only for 1- and 2-axes Wedge Products**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 Vector Form next