What is Double pendulum: Definition and 50 Discussions

In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.

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1. Moment of inertia of a double physical pendulum

I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below
2. Lagrangian of a double pendulum, finding kinetic energy

This is from Taylor's classical mechanichs, 11.4, example of finding the Lagrangian of the double pendulum Relevant figure attached below Angle between the two velocities of second mass is $$\phi_2-\phi_1$$ Potential energy $$U_1=m_1gL_1$$ $$U_2=m_2g[L_1\cos(1-\phi_1)+L_2(1-\phi_2)]$$...
3. Motion Equations by Newton's Formalism for a Double Pendulum

By Lagrange's formalism, the motion equations for double pendulum are: Using Newton's formalism I can't obtain the second equation. Anyone can help?
4. Lagrangian function of a double undamped pendulum

I must find the Lagrangian for an undamped pendulum using the diagram showed below, I've no idea what to do with the second angle φ2 because is measured from the line that joins the two pivot points. The ecuations I must obtain are as follows I get so many different things but I can't reach...
5. Double pendulum equations of motion using Newton's laws

I need help to understand this problem taken from Mechanical Vibrations by S. Rao I know that the equations of motion could be obtained in various ways, for example using the Lagrangian, but, at the moment, I am interested in understanding the method he used. In particular, if I'm not...
6. Discontinuities in a Poincare map for a double pendulum

I'm generating poincare sections of a double pendulum, and they mostly look okay, but some of them have weird discontinuities that seem wrong. The condition for these sections is the standard ##\theta_1 = 0## and ##\dot{\theta}_1 > 0##. Looking at one of the maps, we see that most of the...
7. I Symplectic integrator, non-separable Hamiltonian

I have been attempting to modify a symplectic integrator that I wrote a while ago. It works very well for "separable" hamiltonians, but I want to use it to simulate a double pendulum. I am using the Stormer-Verlet equation (3) from this source. From the article "Even order 2 follows from its...
8. Double pendulum motion (and Lyusternik-Fet Theorem)

Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...
9. Is Double Pendulum taught to all Physics majors?

Is this some esoteric aspect of Physics, that few ever see, or is this part of the common core that almost every Physics major sees? http://scienceworld.wolfram.com/physics/DoublePendulum.html
10. An equilibrium problem -- Spinning a hinged rod and a ball

Homework Statement This is a practice olympiad problem A light rod with length l is hinged in such a way that the hinge folds in one plane only. The hinge is spun with angular speed ω around a vertical axis. A small ball is fixed to the other end of the rod. (a) Find the angular speeds for...
11. MHB Double pendulum: energy function

Hey! :o I am looking at the following: Find the energy function for the double pendulum, with vertical constant and uniform gravity field for motion restricted at vertical plane for motion in space We have that the energy function is the sum of the potential and the kinetic energy...
12. Lagrangian of a double pendulum system (with a spring)

Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...
13. Deriving Kinetic Energy in a Double Pendulum System

Ok, I'm reading up on Lagrangian mechanics, and there is a problem that I don't really understand: the double pendulum (in this case, without a gravitational field). So, I want to take it step by step to make sure I understand all of it. We've got a pendulum (1) with a weight mass m=1kg...
14. What Are the Natural Frequencies of a Double Pendulum Using Torque Methods?

Homework Statement m = 1 kg, l = 1 m, theta 1 and 2 are small I want to work out the natural frequencies (2) of this 2 DOF system through taking torques about the fixed point on the ceiling. I've done it using numerous fixed points and just cannot get the right answer.[/B] Homework...
15. Double Pendulum in C (Trace Motion Real-Time + gif output)?

I have written a C program to trace out the motion of a double pendulum, but am having difficulties in getting gnuplot (controlled from my c program) to trace out the paths of the masses (example video below). Thus far I have created the program such that it produces a number of png images at...
16. Double Pendulum Potential Energy

Hello, everybody. This website and many others define the potential energy of a double pendulum as: V=-(m_1+m_2) g l_1 cos\theta_1-m_2 g l_2 cos\theta_2 However, I came up with the following equation: V= (m_1+m_2) g l_1 (1-cos\theta_1)+m_2 g l_2 (1-cos\theta_2) I started from the position...
17. Plotting Phase Space for Double Pendulum

Homework Statement For a double pendulum, how do we plot the phase space for ##\theta_2## (the lower of the pendulum), i.e. the plot ##\theta_2, \ \dot{\theta}_2?## ##x## = horizontal position of pendulum mass ##y## = vertical position of pendulum mass ##\theta## = angle of pendulum (0 =...
18. Lagrangian for released double pendulum

I just recently worked through the lagrangian method for describing the motion of a double pendulum. What I want to do now is describe the motion of a double pendulum that has been instantaneously released from the origin and allowed to fly through the air (with the 2 pendulums still connected...
19. Double pendulum - solving with energy and Simulink

Hi everyone, I am trying to familiarize myself with Simulink by graphically drawing out differential equations, but ran into a snag with a double pendulum on a cart. Anyways, I neglect friction or other damping effects and say that From there I simply just sum the energies, which ends up...
20. MHB Help with motions of a double pendulum using RK4

Hello everyone, :)I hope you consider this the right place for this question. I have been working way to long on making a model of a double pendulum using the RK4 method with excel. I have these four equations that I should be able plug into RK4 I know that the first two equations for...
21. Poincaré Sections of the double pendulum with Mathematica

I need to plot a Poincaré map for a double pendulum where the string connecting one mass to the other is elastic with elasticity constant k and rest length s. The equations of motions are: \dot{\theta}_1= \frac{p_{\theta_1}}{m_1 r_1^2} - \frac{p_{\theta_2}}{m_1 r_1 r_2} \cos{(\theta _1-...
22. Double Pendulum With Acceleration

Homework Statement You are holding a special pendulum with two masses m_1 and m_2 , instead of one, connected by a rope as shown in Fig. You lower the pendulum such that the tension in the rope between the two masses is half the weight of the bottom mass. Find the acceleration with which...
23. Solving for the eqs of motion for a Double Pendulum using a Lagrangian

Homework Statement Two masses m_1 and m_2 (m_1 ≠ m_2) are connected by a rigid rod of length d and of negligible mass. An extensionless string of length l_1 is attached to m_1 and connected to a fixed point P . Similarly, a string of length l_2 (l_1 ≠ l_2) connects m_2 and P...
24. Runge-Kutta Method for a double pendulum

Hello, I am trying to program a double pendulum via the 4th order Runge-Kutta method and I cannot seem to be getting the right output. At first I used the Euler-Cromer method, but now I am aiming to make it more accurate. Homework Statement I have the equations of motion: d(omega)/dt and...
25. How can I represent a double pendulum system using matrices?

Homework Statement See attached link The Attempt at a Solution I would have write my work out here, but I have not managed to display matrices next to each other yet. My problem is putting it into matrix form. The form I have is shown in the below attachement. The matrix I get for...
26. Mathematica Mathematica: Graphing The behavior of a double pendulum

Hello, I have a few newb questions. How can I graph the behavior of a double pendulum in Mathematica to make strange attractors like in the Lorenz equations?
27. Equations of motion of a double pendulum

Hello, This is my first post on this forum, so please excuse me if I am not clear enough. I have recently been fascinated about chaos and decided to learn about the equations of motion in a double pendulum. I am in high school and have been so interested about chaos and its equations of motion...
28. Double Pendulum (One pendulum hanging from the other)

Homework Statement A body of mass m hangs by a light inelastic string of length a from a body of mass 3m which in turn hangs from a fixed point O by a string of length a. The masses are confined to motion in a vertical plane through O. Denote the horizontal displacements of the two particles...
29. Hamilton's equations for double pendulum

At the bottom of the following website are the 4 equations that I am using for a double pendulum simulation. http://scienceworld.wolfram.com/physics/DoublePendulum.html The equation for C2 has the variables P1 and P2 and I can't work out what they are.:confused: Is it a typo and they are...
30. Double pendulum equations of motion

Hi, I am trying to create displacement time series graphs of a double bar pendulum using Matlab. Am I correct in assuming that if I use the ode45 solver to integrate the equations below I can plot displacement time series graphs? Are these the correct coupled first order ODEs to use...
31. Angular constraints on the Inverted Double Pendulum - 'Acrobot'

I am attempting to recreate Sutton's work on the 'Acrobot' and have modeled a good solution to the following: http://webdocs.cs.uAlberta.ca/~sutton/book/ebook/node110.html The physics is implemented in exactly the same way, however my particular Java implementation requires some constraint...
32. What Is the Kinetic Energy Equation for a Mass on a Double Pendulum?

You can treat the cable as another rigid bar in this case, both massless. I just need the equation for the Kinetic Energy of the mass on the end. Is there an equation for if the main bar is torqued at a given τ(t), and any other necessary information is given, to find the position of the mass...
33. Mathematica Mathematica: Differential equations for double pendulum

Hello Im new here, I hope I'm not disturbing anyone. Following this guide below, I am trying to find two 2. order differential equations, one for q1'' and one for q2'', describing the movement of the double pendulum. I have no problems with the mathematics, but when the guide tells me to...
34. Double Pendulum Motion: Plotting theta2 vs Time

Hello all, I have written a python code implementing the Runge-Kutta fourth order method for higher orders to approximate the motion of a double pendulum. The problem I am having is that my plot of theta2 (angle of second rod) Vs time looks a little off and I am curious if I have it correct...
35. Double Pendulum and Normal Modes (Kibble problem)

Homework Statement 1. A double pendulum, consisting of a pair, each of mass m and length l, is released from rest with the pendulums displaced but in a straight line. Find the displacements of the pendulums as functions of time. === So... this is a problem from Kibble's Classical Mechanics...
36. Double Pendulum Generalized Coordinates

The picture for the double pendulum I am referring to is pretty standard, wikipedia for example uses it and so does any other textbook. I do not completely understand why one uses the second angle measured from the vertical y-axis for the second generalized coordinate. The second angle is not...
37. Wave Mechanics Problem Double Pendulum and a Spring

I'm in a wave mechanics class and a homework assignment asks us to describe what would happen if a driving force is applied to m1, m2, or both. The explanation should be both calculational and written. I have no idea how to model this system in equation form! Help!
38. Double pendulum velocity derivation

I'm doing a personal project and I'm refreshing my knowledge on Lagrangian mechanics. Right now, I am looking at the double pendulum example. How is the velocity of the 2nd mass derived, in terms of the angles of the two rods? 2nd mass as in, the mass that hangs lowest. I have not been...
39. Double pendulum, time question

I'm probably going to learn about the double pendulum in a few weeks, however I have a question that I can't get rid off from my head. Is there a time (I imagine it to be very large) where the pendulum reach the initial position/configuration? In another words, a time where it moves as it...
40. Double Pendulum Problem - Lagrangian

Homework Statement Rather than solve the double pendulum problem with two masses in the usual way. Instead express the coordinates of the second mass, in terms of the coordinates of the mass above it. $x2=x_1+\xi = L_1Sin[\theta]Cos[\phi]+L_2Sin[\alpha]Cos[\beta]$\\ \$ y2=y_1+ \eta =...
41. Solve Double Pendulum Beat Period Calculation

Double Pendulum URGENT! Homework Statement I am trying to solve this past paper question for my exam tomorrow: A double pendulum is constructed using a light rod and light inextensible strings. Two string pendulums hanging from ceiling 1m long. 0.1m from top they are connected by a light...
42. Double Pendulum with motor between segments

Hello everyone, First, I must apologize in advance as I am no physicist, and am unable to be of any help in physics to anyone else at a high level. I have a general knowledge of a wide range of subjects, and I have a problem that I need to understand better. So, with that said, here is my...

Homework Statement I have to get the equations of motion for the double pendulum and then represent it in State Space form. Homework Equations Now as you can see in the check.jpg attachment, i assumed earlier that both pendulum rods have the same length and both pendulums have the...
44. Double Pendulum Lagrange's Equation Problem

Homework Statement A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths and have bobs of equal mass and if both pendula are confined to move in the same plane, find Lagrange's equations of motion for the...
45. Applying torque to a double pendulum

If you apply a torque t to a double pendulum with masses and lengths, m1. m2, l1, and l2, what is the torque experience by each individual mass?
46. Finding the Time Period of a Double Pendulum

does the double pendulum have a time period as such...and if so...how do we practically find it out...and if so then the time period is dependant on the intermediate mass or the main bob?
47. Double Pendulum Mass & Distance Effects on Period

I was wondering how the time period of a double pendulum depends on the mass of the intermediate object and its distance from the bob?
48. Double Pendulum Homework: Small Angle Approximation

Homework Statement A double pendulum consists of light, inextensible strings, AB and BC each of length l. It is fixed at one end A and carries two particles, each of mass m, which hang under gravity. The pendulum is constrained to move in a vertical plane. The angle between the vertical and AB...
49. Generalized Coordinates: Double Pendulum

Homework Statement Standard double pendulum setup. A string with mass, connected to a string with a mass, mounted to the ceiling. Given is m1,m2,l1,l2 a) choose a suitable set of coordinates and write a lagrangian function, assuming it swings in a single vertical plane (I did this, using L...
50. Solving Double Pendulum Motion w/ Hit on Lower Rod

If you have have double pendulum of two rods where the rods moves with the same frequency w at the equilibrium position and at the eq. position you hit the lower rod at a distance d from the point that connects the rods. The hit results in a motion where the upper rod moves with frequency w and...