Double Pendulum
The benefits of generalized coordinates become apparent with the analysis of a double pendulum. For the two masses mi, i=1, 2, let r=(xi, yi), i=1, 2 define their two trajectories. These vectors satisfy the two constraint equations,
The formulation of Lagrange's equations for this system yields six equations in the four Cartesian coordinates xi, yi i=1, 2 and the two Lagrange multipliers λi, i=1, 2 that arise from the two constraint equations.
Read more about this topic: Generalized Coordinates
Famous quotes containing the words double and/or pendulum:
“I know [my label], in any case: a double face, a charming Janus, and underneath, the house motto: Be wary. On my business cards: Jean-Baptiste Clamence, actor.”
—Albert Camus (19131960)
“The pendulum oscillates between these two terms: Sufferingthat opens a window on the real and is the main condition of the artistic experience, and Boredom ... that must be considered as the most tolerable because the most durable of human evils.”
—Samuel Beckett (19061989)