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Topic: Double pendulum

	Double Elliptical Pendulum Harmonograph
		I was most interested in the Double Elliptical Pendulum Harmonograph because of the striking complexity of the patterns it could produce.
		The handsomest patterns are generated when the frequency of the upper pendulum bears a whole-number ratio to that of the lower pendulum - a ratio such as 3:2 or 2:1.
		The adjustable factors that describe any given figure are then the two amplitudes of the upper pendulum, the phase angle between them, the phase between upper and lower pendulum, the phase and amplitudes of the lower pendulum and the ratios of the frequencies of the upper and lower pendulums.
	www.lclark.edu /~miller/harmonograph.html (1005 words)

	Reference.com/Encyclopedia/Pendulum
		The isochronism of the pendulum suggested a practical application for use as a metronome to aid musical students, and possibly for use in a clock.
		The mass of the pendulum was 28 kg and the length of the arm was 67 m.
		As the angles increase, however, the double pendulum exhibits chaotic motion that is sensitive to the initial conditions.
	www.reference.com /browse/wiki/Pendulum (1778 words)

	Chaotic Pendulum Physics Simulation
		The pendulum is modeled as a point mass at the end of a massless rod.
		The damping (friction) is proportional to the angular velocity of the pendulum.
		This is the equation of motion for the driven damped pendulum.
	www.myphysicslab.com /pendulum2.html (620 words)

	Second Push - Double Push -Speedskating Santa Barbara
		The inverted pendulum requires that the string be replaced with a thin stiff rod and that appropriate sideways forces be applied at ground level or the inverted pendulum will fall to the ground without executing even one oscillation.
		The simple pendulum has an oscillating motion with frequency of oscillation depending on the square root of g/L (g is gravitational acceleration, L is the length of the suspension string, cable, or rod).
		So a real pendulum has a damped oscillation and gravity does not only not drive an accelerating motion, it cannot even maintain a steady motion unless some external driving force is added, say from a pulsed electromagnet to replace the friction losses.
	home1.gte.net /pjbemail/SecondPush.html (1912 words)

	Search Results for "pendulum"
		...A pendulum clock having a round face, a relatively narrow elongated case, and a rectangular box at the bottom....
		It has a double pendulum whose pace can be altered by sliding the upper weight up or down....
		In the harmonic motion of a pendulum, the amplitude of the swing is the greatest distance reached...
	www.bartleby.com /cgi-bin/texis/webinator/sitesearch/+9wwFqopnDm1c1MxzmAwwwqFqqmx (316 words)

	[No title]
		The double pendulum is a popular device for demonstration of deterministic chaos.
		This grease hinders rotation of the bearing and therefore movement of the pendulum.
		As with all pendulums, your double pendulum's oscillations are affected by friction and the moment of inertia of the components.
	www.rose-hulman.edu /~moloney/AppComp/2000Entries/Entry16/Entry16.htm (1743 words)

	Pendulum principle demonstration apparatus (US5145378)
		A base supports a vertical pivot arm, one end of which supports a pivotal rotation means for a rotation support housing with a plurality of radial connector sockets.
		One of several pendulum arms can be fitted into each of the radial connector sockets, the pendulum arms supporting a pendulous mass on each pendulum arm.
		One such pendulum arm is articulated into two portions, each portion with a plurality of additional pendulum arms attached thereto.
	www.delphion.com /details?pn=US05145378__ (319 words)

	Print the story
		A double pendulum consists of one pendulum tacked on to the end of another.
		The upper pendulum swings from a fixed pivot point and the lower pendulum swings from the end of the upper one.
		In golf, the equivalent components are the shoulders (acting as the fixed pivot), arms and hands (the upper pendulum), and the club shaft and club head (the lower pendulum).
	www.physorg.com /printnews.php?newsid=85663321 (665 words)

	Running Mechanical Models (SimMechanics)
		The joint connecting the upper and lower arms of this pendulum contains a torsional spring and damper system that exert a counterclockwise force directly proportional to the angular displacement and velocity of the joint, respectively.
		This model uses Body blocks to model the upper and lower arms of the pendulum and a Revolute Joint block (J1) to model the connection between the pendulum and ground.
		In the case of the double pendulum, the point [0; 0; 0; 0] (i.e., the pendulum initially folded up and stationary) is a trivial equilibrium point and therefore to be avoided.
	www.weizmann.ac.il /matlab/toolbox/physmod/mech/mech_running7.html (1007 words)

	Double Pendulum
		Double Pendulum: A Bridge Between Regular Dynamics and Chaos
		Abstract: Of all physical phenomena, the simple pendulum is perhaps the best suited to introduce students to the concept that the natural world can be described in a mathematical language and provides an entry point into conceptual, analytic and experimental techniques.
		The double pendulum is a system that behaves exactly like the simple pendulum for small amplitudes but is chaotic for larger amplitudes providing students with an introduction to the fascinating ideas about chaos theory while tying it closely to concepts and techniques taught at the Regents Physics level.
	www.cns.cornell.edu /cipt/labs/DoublePendulum.html (156 words)

	Double pendulum - Tabitha
		It turns out that the simple double pendulum is pathological, so we will have to be a bit more sophisticated in our modelling of this system.
		For example, we could plot whether either pendulum flips within a set period of time as a function of the initial conditions to see the general structure of the solutions.
		Outside this region, the pendulums can flip but this is different from determining when they will flip.
	tabitha.phas.ubc.ca /wiki/index.php/Double_pendulum (515 words)

	Double Pendulum
		Because the double pendulum is a Hamiltonian system (a conservative system) where the energy of the system is conserved, one must use numerial integration methods which conserve the energy.
		On the left side, the behaviors of the double pendulum is displayed.
		Because the double pendulum is a Hamiltonian system (a conservertive system), there exist no attractors, and tori or chaotic seas would be observed.
	brain.cc.kogakuin.ac.jp /~kanamaru/Chaos/e/DP (219 words)

	The Double Pendulum
		The double pendulum is composed of a second pendulum attached to the end of the bob of an initial simple pendulum, as shown in the diagram below:
		As a result, the motion of the pendulum is more difficult to model, and requires more complex mathematics than those used to simulate the motion of the Simple Pendulum.
		In addition to this, it is also possible to activate a trace on the second bob in order to make it easier to visualise the motion of the pendulum over time; and you can deactivate gravity to see how the pendulum would react in zero-gravity conditions.
	www.maths.surrey.ac.uk /explore/michaelspages/Double.htm (201 words)

	Double Pendulum
		Each mass plus rod is a regular simple pendulum, and the two pendula are joined together and the system is free to oscillate in a plane.
		The left panel shows two animated gifs illustrating solution of these equations for one kilogram pendulum masses and one metre pendulum lengths, for the indicated times in seconds (the two gifs may take some time to load - they are 109kB and 239kB respectively).
		The School of Physics at the University of Sydney has a compound square double pendulum.
	www.physics.usyd.edu.au /~wheat/dpend_html (267 words)

	Chaotic Pendulums - Chaos Theory & The Double Pendulum
		However, unlike a simple single pendulum, it is impossible to predict the long term behaviour of the double pendulum.
		Put another way, the behaviour of a chaotic system depends so sensitively on the system's precise initial conditions that it is, in effect, unpredictable and cannot be distinguished from a random process, even though it is deterministic in a mathematical sense.
		To experience chaos theory first hand, repeatedly spin your chaotic pendulum ensuring that you have all initial conditions (initial position, initial angles, initial force) as closely matched to the previous experiment as possible.
	www.chaoticpendulums.com /chaos-theory-a9.html (364 words)

	Running Mechanical Models (SimMechanics)
		Consider a double pendulum initially hanging straight up and down.
		The net force on the pendulum is zero in this configuration.
		It is therefore unnecessary to pass any additional arguments (other than the model's name) to the command to linearize the model.
	www.technion.ac.il /guides/matlab/toolbox/physmod/mech/mech_running9.html (482 words)

	Pendulum and Cart Physics Simulation
		We consider the torque from friction of the pendulum to be a vector perpendicular to the plane where the pendulum and cart move.
		This torque force F is applied at the pendulum bob, and its opposite is applied at the cart.
		You will find the same "Mass and Plane Pendulum Dynamic System" discussed on page 234 of the 1996 edition.) Our first step is to find the Lagrangian of the system which is the kinetic energy minus the potential energy.
	www.myphysicslab.com /pendulum_cart.html (2131 words)

	Linearizing Mechanical Models :: Analyzing Motion (SimMechanics)
		Right-multiplying A by the state vector x yields the differential state equations corresponding to the LTI model of the double pendulum,
		These modes characterize how the double pendulum responds to small perturbations in the vicinity of the operating point, which here is the force-free equilibrium.
		The preceding sections of this chapter, Inverse Dynamics Mode with a Double Pendulum and Constrained Trimming of a Four Bar Machine, discuss the inverse dynamics and trimming of the four bar system.
	www.mathworks.com /access/helpdesk/help/toolbox/physmod/mech/f0-6469.html (1847 words)

	YouTube - Double Pendulum
		Join YouTube for a free account, or log in if you are already a member.
		A double pendulum is a simple but effective dem...
		A double pendulum is a simple but effective demonstration of chaos theory.
	www.youtube.com /watch?v=8VmTiyTut6A (221 words)

	Math Forum Discussions - Re: 3D Double Pendulum Simulation
		>of a double pendulum in 3 dimensions driven by external torques.
		the double pendulum can show up chaotic behaviour, that means minimal changes
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.com /kb/thread.jspa?forumID=226&threadID=1419650&messageID=4950239 (390 words)

	Double Pendulum -- from Eric Weisstein's World of Physics
		Double Pendulum -- from Eric Weisstein's World of Physics
		A double pendulum consists of one pendulum attached to another.
		Double pendula are an example of a simple physical system which can exhibit chaotic
	scienceworld.wolfram.com /physics/DoublePendulum.html (140 words)

	Double Pendulum/Iron Byron
		However, it goes on to translate the swing to what a person would have to do to implement the same principles given the differences between a model and a person.
		Well iron byron is a double pendulum but rather than being gravity powered (like what you've shown above) its powered by a motor at the hub (fl dot).
		Jorgeson used a double pendulum with a torque but he let the hub (fl dot) move.
	www.activegolf.com /forums/fb.aspx?go=prev&m=2130300&viewType=tm (989 words)

	Encyclopedia :: encyclopedia : Pendulum (Site not responding. Last check: )
		A gravity pendulum (plural pendula) is a weight on the end of a rigid rod (or a string/rope), which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point.
		The pendulum was discovered by Ibn Yunus al-Masri during the 10th century, who was the first to study and document its oscillatory motion.
		The blue arrow is the gravitational force acting on the bob, violet arrows are that same force resolved into components parallel and perpendicular to the bob's instantaneous motion, the motion along the red axis, which is always perpendicular to the cable/rod.
	www.hallencyclopedia.com /Pendulum (1260 words)

	Pendulum - Wikipedia, the free encyclopedia
		The pendulum was discovered by Ariana Leane during the 10th century, who was the first to study and document its oscillatory motion.
		A pendulum whose time period is two seconds is called the second pendulum since most clock escapements move the seconds hands on each swing.
		A pendulum in which the rod is not vertical but almost horizontal was used in early seismometers for measuring earth tremors.
	en.wikipedia.org /wiki/Pendulum (552 words)

	Pendulum
		A simple gravity pendulum (plural pendulums or pendula), also called a bob pendulum, is a weight on the end of a rigid rod (or a string/rope), which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point.
		is the semi-amplitude of the oscillation, that is the maximum angle between the rod of the pendulum and the vertical.
		Pendulums (these may be a crystal suspended on a chain, or a metal weight) are often used for divination and dowsing.
	www.brainyencyclopedia.com /encyclopedia/p/pe/pendulum.html (1418 words)

	NationMaster - Encyclopedia: Pendulum (Site not responding. Last check: )
		A double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior.
		Katers pendulum is a reversible pendulum designed and built by Captain Henry Kater in 1817 to measure the acceleration of free fall so that gravity may be calculated without knowledge of the pendulums centre of gravity and radius of gyration.
		In the case of a pendulum with a point mass swinging on massless string or rod of length l, and an ambient gravity acceleration of g, the period of a complete oscillation is
	www.nationmaster.com /encyclopedia/Pendulum (1170 words)

	Pendulum (Site not responding. Last check: )
		For small displacements the movement of an pendulum can be described mathematically as simple harmonic motion as the change in potential energy the bottom of a circular arc is proportional to the square of the displacement.
		pendulums will also lose energy as they and so their motion will be damped the size of the oscillation decreasing approximately exponentially with time.
		In the case of a pendulum with point mass swinging on a massless rigid rod length l where $\theta is the angle between rod and the vertical the acceleration is by g\cdot sin\theta and is equal to angular acceleration multiplied by the length of rod.$
	www.freeglossary.com /Pendulum (1056 words)

	NationMaster - Encyclopedia: Double pendulum (Site not responding. Last check: )
		The motion of a double pendulum is governed by a set of coupled ordinary differential equations.
		The position of the centre of mass of the two rods may be written in terms of these coordinates.(If the origin of the coordinate system is assumed to be at the point of contact of the wall and the first pendulum).
		The double pendulum undergoes chaotic motion, and shows a sensitive dependence on initial conditions.
	www.nationmaster.com /encyclopedia/Double-pendulum (1148 words)

	> > L'eStudiolo de Pendulum > >
		When you make a pendulum its periodicity, that is to say the time it takes to make one complete oscillation, depends solely on the length of the wire or rod that supports it and on the force of gravity in the place where it is hung.
		The pendulum swings faster the closer it is to the centre of the earth, independent of its mass and the width of its oscillation.
		The movement of the pendulum is the result of the limitations in the degrees of freedom of the movements of each one of the oscillation points.
	www.pendulum.es /english/estudiolo/pendulos.html (1684 words)

	Pendulum (Site not responding. Last check: )
		Pendulum is a trade name for a preemergent herbicide used for control of crabgrass in turf.Its active ingredient is pendimethalin.
		For small displacements, the movement of an ideal pendulum can be described mathematically as simple harmonic motion, as the change in potential energy atthe bottom of a circular arc is nearly proportional to the square of the displacement.
		In the case of a pendulum with a point mass swinging on a massless rigid rodof length l, where θ is the angle between the rod and the vertical, the accelerationis given by
	www.therfcc.org /pendulum-20465.html (682 words)

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