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http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/PendulumWithMovingSupport.pdf
A pendulum with a moving support point Gabriela Gonz´alez September 12, 2006 Consider a pendulum with mass m hanging from a rod of length l. The support point moves horizontally with a known function R(t) = X(t)ˆi + Y(t)ˆj. We can use the angle θ between the vertical and the pendulum rod as a generalized coordinate, the only one
https://en.wikipedia.org/wiki/Lagrangian_mechanics
Lagrangian mechanics is widely used to solve mechanical problems in physics and when Newton's formulation of classical mechanics is not convenient. Lagrangian mechanics applies to the dynamics of particles, while fields are described using a Lagrangian density. Lagrange's equations are also used in optimization problems of dynamic systems.
https://www.youtube.com/watch?v=xZVbDDhhRYA
Nov 10, 2013 · The mass of the support equals the mass of the bob. The initial angular velocity of the bob is given by: 2.9√(g/l) so that the pendulum barely has enough energy to go over the top.Author: Don Burgess
https://www.myphysicslab.com/pendulum/moveable-pendulum-en.html
Physics-based simulation of a pendulum attached to a moveable support point or "anchor block". The support point is assumed to be so massive that it is not affected by the pendulum. You can drag the anchor block or pendulum with your mouse. Change parameters like …
https://www.youtube.com/watch?v=YpDDkzg3U4o
Jan 13, 2014 · Café Planck is the result of many years of effort in the field of mathematics and physics tutoring in all level of education. Our goal is to teach you how to employ Mathematica to learn and ...Author: C Planck
https://en.wikipedia.org/wiki/File:PendulumWithMovableSupport.svg
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http://www.physics.usu.edu/torre/6010_Fall_2010/Lectures/03.pdf
third term in the Lagrangian represents a coupling of the velocities of the two masses through the kinetic energy. This is a consequence of interaction of the pendulums induced by the constraints discussed above. Example: Plane pendulum with moving support. Consider a plane pendulum (mass m2, length l) whose point of support is a mass
https://engr.iupui.edu/~skoskie/ECE680/ECE680_l3notes.pdf
of a cart with inverted pendulum. Instead of using the Lagrangian equations of motion, he applies Newton’s law in its usual form. There are a couple of differences between the examples. Specifically, in the example in Section 1.7 1. the pendulum is a distributed rather than point mass, and 2. frictional force on the cart wheels is considered.
https://www.physicsforums.com/threads/lagrangian-for-pendulum-with-moving-support.944782/
Apr 14, 2018 · Lagrangian for pendulum with moving support Thread starter Decimal; Start date Apr 14, 2018; Apr 14, 2018 #1 Decimal. 60 6. Homework Statement [/B] In a homogeneous gravity field with uniform gravitational acceleration g, a pointmass m1 can slide without friction along a horizontal wire. The mass m1 is the pivot point of a
http://www.aoengr.com/Dynamics/LagrangianMechanicsPendulum.pdf
Lagrangian mechanics to see how the procedure is applied and that the result obtained is the same. For this example we are using the simplest of pendula, i.e. one with a massless, inertialess link and an inertialess pendulum bob at its end, as shown in Figure 1. Figure 1 – Simple pendulum Lagrangian formulation The Lagrangian function is ...
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