Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

User Tools

Site Tools


book:chap6:6.3_dynamics_with_one_degree_of_freedom

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
book:chap6:6.3_dynamics_with_one_degree_of_freedom [2022/02/14 14:03] abrilbook:chap6:6.3_dynamics_with_one_degree_of_freedom [2022/04/12 13:53] (current) abril
Line 255: Line 255:
 This EOM can once be integrated by the same strategy adopted for the swing and the spherical pendulum. This EOM can once be integrated by the same strategy adopted for the swing and the spherical pendulum.
 Thus, one finds the effective potential  Thus, one finds the effective potential 
 +<wrap #eq_EOMpearlRing-Ueff></wrap>
 \begin{align*}  \begin{align*} 
   U_{\text{eff}}(\theta) = -\omega^2\; \cos\theta \; \left[ 1 - \left( \frac{\Omega}{\omega}  \right)^2  \; \cos\theta \right] \tag{6.3.5}   U_{\text{eff}}(\theta) = -\omega^2\; \cos\theta \; \left[ 1 - \left( \frac{\Omega}{\omega}  \right)^2  \; \cos\theta \right] \tag{6.3.5}
book/chap6/6.3_dynamics_with_one_degree_of_freedom.1644843819.txt.gz · Last modified: 2022/02/14 14:03 by abril