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Topic: Spherical pendulum

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	Pendulum (via CobWeb/3.1 planetlab03.cs.washington.edu) (Site not responding. Last check: 2007-09-29)
		For smaller displacements, the movement of an ideal pendulum can be described mathematically as simple harmonic motion, as the change in potential energy at the bottom of a circular arc is nearly proportional to the square of the displacement.
		Real pendulums will also lose energy as they swing, and so their motion will be damped, with the size of the oscillation decreasing approximately exponentially with time.
		The case of a pendulum with a point mass swinging on a massless rigid rod of length l is the simple gravity pendulum ('''simple pendulum''').
	pendulum.kiwiki.homeip.net.cob-web.org:8888 (893 words)

	Non-classical Pendula
		The trace was produced by connecting the SDC sensor of the pendulum to an x-y recorder and letting the pen follow the motion of the pendulum in free decay.
		To sense the motion of this pendulum, a velocity detector is employed in which two rare earth magnets are placed on a Be-Cu cantilever and positioned on opposite sides of an aluminum disk mounted on the motor shaft which is the axis of the pendulum.
		The tiltmeter is a torsion pendulum having some similarities to the torsion-gravity pendulum, however it is designed to operate away from the double well of the latter.
	physics.mercer.edu /petepag/pend.htm (2337 words)

	[No title]
		We suspect the period could depend on at least the following factors: (1) mass of the pendulum bob, (2) shape of the bob, (3) volume of the bob, (4) length of the suspension string, (5) air resistance (drag) on the bob and string, (6) size of the swing (amplitude), (7) Size of the gravitational force.
		Pendulum bobs of equal radius, but different masses, made of cork, wood, brass, steel, etc.; string, one- and two-meter sticks; electric stop clock; balance scales; goniometer (on the back of this lab manual); 2 x 1 cycle log-log graph paper.
		A spherical pendulum is one in which the bob swings in a perfect circle in a horizontal plane.
	www.lhup.edu /~dsimanek/scenario/labman1/pendulum.htm (1662 words)

	Pendulum
		When the position of a mass is changed on the pendulum rod or the position of one of the points is adjusted so that the period in both positions is the same, the length of the equivalent simple pendulum is equal to the distance between the supports.
		The bifilar pendulum is a simple or physical pendulum which is suspended from two points so that it is constrained to oscillate about a fixed horizontal axis through the line joining the two points of suspension rather than having the freedom to move in any direction.
		The Blackburn pendulum is a bifilar pendulum in which the lower part is another pendulum supported by a single string attached to the V formed by the upper pair of strings.
	www.arts.unsw.edu.au /pendulum/bibliography.html (11263 words)

	Modern Vastu (Energy) Science, India (Site not responding. Last check: 2007-09-29)
		We use the term Pendulum Querying System as we believe that the Pendulum responds to the Energy Force Field of the subject or object of enquiry and thus merely reveals the present condition of the Energy Force Field in terms of Positive or Negative state of its Energy Force Field.
		Pendulum Querying System developed by Daya Dhaar Self Care Center offers indications by certain peculiar movements of the Pendulum, to draw the attention of the Dowser, in case of any mistake by the Dowser, thus preventing the chances of any mis-interpretation and mistakes.
		Pendulum Dowsing leads to spontaneous harmony and happiness in the life of the dowser as also his network of associations or connections.
	www.harmony000.org /pendulum/faq.htm (3082 words)

	Pendulum - Wikipedia, the free encyclopedia
		A simple gravity pendulum or bob pendulum (plural pendulums or pendula), is a weight (or bob) 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 length of the pendulum measured from the pivot point to the bob's center of gravity.
		See pendulums for divination and dowsing for a more detailed discussion.
	en.wikipedia.org /wiki/Pendulum (678 words)

	Simple Harmonic Motion
		With a 200 g mass on the stiffer spring, the spring mode and pendulum mode are parametrically coupled.
		A pendulum whose length is equal to the displacement of a spring from equilibrium when the weight is attached has the same period of oscillation as the spring.
		The spring mode parametrically drives the penduIum mode, but the pendulum motion causes the tension in the spring to vary at twice the pendulum frequency, and therefore resonantly drives the spring mode.
	www.physics.ucla.edu /demoweb/demomanual/harmonic_motion_and_waves/simple_harmonic_motion/simple_harmonic_motion.html (496 words)

	Spherical pendulum biography .ms (via CobWeb/3.1 planetlab03.cs.washington.edu) (Site not responding. Last check: 2007-09-29)
		A spherical pendulum is a generalization of the pendulum.
		The only forces acting on the mass are the reaction from the sphere and gravity.
		It is convenient to use spherical coordinates and describe the position of the mass in terms of
	www.biography.ms.cob-web.org:8888 /Spherical_pendulum.html (52 words)

	Phys 103 - The Simple Pendulum - Fall 2006
		The period of a pendulum is determined by its length.
		You are given a pendulum with a support with which you can adjust the length of the string, and a photogate.
		Period (T): In the "PEND" (pendulum) mode the timer will display the time interval for one full swing, the period T of the pendulum (the light interruption during the backswing is ignored).
	it.stlawu.edu /~physics/labs/103_lab/html/pendulum.shtml (959 words)

	The Spherical Pendulum (Site not responding. Last check: 2007-09-29)
		The spherical pendulum is similar to the Simple Pendulum, except that it moves in 3-dimensional space.
		The spherical pendulum is shown in the diagram below:
		Note that the (x, y, z) axes are displayed on the applet to make it more obvious as to how the pendulum is oriented, and that the y-axis is coming out of the screen.
	www.maths.surrey.ac.uk /interactivemaths/michaelspages/Spherical.htm (161 words)

	Abstract: The triple-spherical pendulum
		In this report, the derivation and analysis of the triple-spherical pendulum is considered.
		The stability of these relative equilibria are then considered by applying the energy-momentum method, and results showed that there are two bifurcation parameters and four relative equilibrium solutions, of which one is the trivial rotation and the remaining are ``cowboy'' solutions.
		In particular, for the case of $r=1$, $\hat{r}=1$, $m=2$, and $\hat{m}=1$, there is only one stable ``cowboy'' solution and it resembles the double-spherical pendulum case in which the upper two beads portion acts like a single string with a mass.
	avalon.caltech.edu /~cxy/proj_141a.html (126 words)

	[No title]
		You will compare the measured period of a real pendulum (spherical ball suspended from a string) with the expected period of an ideal pendulum (point mass suspended from a massless string), as determined from Newton’s second law.
		Period (T): In the “PEND” (pendulum) mode the timer will display the time interval for one full swing, the period T of the pendulum (the light interruption during the back swing is ignored).
		Release the pendulum, let it swing once or twice to settle into its natural motion, then press the reset button on the timer to begin collecting data.
	it.stlawu.edu /~physics/labs/103_lab/docs/pendulum.doc (1258 words)

	Tiffany Never Wind / Early Models
		Later styles in polished brass "crystal regulator" style cases appeared, but the most common to survive are the original glass dome style with spherical ball torsion pendulum.
		A new design completely different from the original spherical ball pendulum bob model clocks appeared during the late 1920s.
		The pendulum is propelled only in one direction, a single self-wiping electrical contact is employed, the electromagnets are much smaller and the frame and base of these less expensive versions are steel stampings with gold colored electroplating over copper underlayment.
	www.greaterlaregional.com /exhibits/2003exhib/23.html (329 words)

	Example: Spherical pendulum (Site not responding. Last check: 2007-09-29)
		Let us consider the idealized spherical pendulum presented in figure 5.1.
		Assuming that all initial conditions are known, we have to derive the equations of motion of the mass under the influence of gravity.
		Given the initial position and velocity of the center of mass, equation (5.7) uniquely describes the motion of the pendulum.
	icosym-nt.cvut.cz /odl/partners/fuh/course_main/node23.html (111 words)

	Assignment 4 (Site not responding. Last check: 2007-09-29)
		For the spherical shell: a = (3/5) gsinq.
		Obtain Lagrange's equations of motion for a spherical pendulum (a mass point suspended by a rigid, weightless rod).
		A simple pendulum of length b with a bob of mass m is attached to a massless support moving horizontally with constant acceleration a.
	electron9.phys.utk.edu /phys513/Assignments/h4s.htm (1183 words)

	Dynamics and Chaos: The Spherical Pendulum (Abstract) (Site not responding. Last check: 2007-09-29)
		A simple dynamical system, the spherical pendulum, is introduced to illustrate issues, principles, and effects of chaos in dynamics.
		The spherical pendulum is a two degrees of freedom nonlinear system with a pivot point in space.
		The equations of motion for the pendulum are derived, simulated, and animated.
	www.eg.org /EG/CGF/volume15/issue4/v15i4pp263-270_abstract.html (114 words)

	8 Friction Pendulum Seismic Isolation Bearings for Buildings, Bridges, Industrial Facilities
		With spherical Friction Pendulum seismic isolation bearings at each support point, a structure sways with a gentle pendulum motion during earthquake ground shaking.
		Friction Pendulum bearings are simple in design but with versatile properties and a wide range of ap-plications.
		Friction Pendulum bearings have been used in some of the world’s largest seismically isolated buildings, bridges, and industrial tanks.
	www.cif.org /nominations/nom_338.html (131 words)

	A Spherical Pendulum System To Teach Key Concepts in Kinematics, Dynamics, Control, and Simulation
		The Rice Spherical PENDUlum Laboratory APparatus (SPENDULAP) is a rich teaching aid for senior and first year graduate courses in kinematics, dynamics, control, and simulation.
		It consists of a free- swinging (un-actuated) rigid pendulum mounted in a rotating frame.
		The spherical pendulum is sufficiently complex to demonstrate the advantages of the Lagrangian approach, and it also offers an excellent illustration of the benefits of the Newtonian formulation.
	www.ewh.ieee.org /soc/es/Nov1999/05/BEGIN.HTM (581 words)

	The spherical pendulum
		This, of course, is the equation of a simple pendulum whose motion is restricted to the vertical plane
		, the pendulum bob rotates uniformly in a horizontal plane.
		This type of pendulum is usually called a conical pendulum, since the string attached to the pendulum bob sweeps out a cone as the bob rotates.
	farside.ph.utexas.edu /teaching/336k/lectures/node84.html (324 words)

	No Title
		A spherical pendulum consists of a bob of mass m and a weightless rod of length l.
		One end of the rod is fixed at the origin, while the other is attached to the bob, so that the bob pivots in any direction about the origin, yet always remains at fixed radius l.
		The bob thus moves on a spherical surface of radius l, subject to gravity.
	www.emory.edu /PHYSICS/Faculty/Benson/254/hw7/hw7.html (447 words)

	Spherical Pendulum (via CobWeb/3.1 planetlab03.cs.washington.edu) (Site not responding. Last check: 2007-09-29)
		The spherical (gravitational) pendulum has its state determined by 4 numbers, once the length of its rigid and weightless supporting rod is fixed.
		Allowed to move subject to the force of gravity, the basic equation of motion is Newton's equation.
		Analytically, it is easy to implement this is with the Euler-Lagrange equations for the motion of the pendulum, considered as a particle constrained to move in a sphere under a conservative force.
	www.mathwright.com.cob-web.org:8888 /gallery/bk3d004.html (171 words)

	SPENDULAP, Introduction; F. Ghorbel, J.B. Dabney
		The pendulum is mounted in a motor-drive frame inside an acrylic housing.
		The pendulum features an initial position mechanism that allows one to initiate frame rotation with the pendulum at an arbitrary deflection about the swing axis.
		The control task is to design a feedback control law which adjusts drive motor torque to cause the pendulum to stabilize at a preselected deflection angle.
	www.ewh.ieee.org /soc/es/Nov1999/05/1.html (860 words)

	The Taipei 101 Tower, Taiwan: The Tallest Building in the World
		The weld between each constitutent slab of steel in the spherical pendulum.
		Professor L. Hsiung in front of the spherical pendulum.
		Chun Chen Wei and Professor Chin-Huai Young in front of the spherical pendulum.
	www.msm.cam.ac.uk /phase-trans/2005/t101/t101.html (1576 words)

	spherical pendulum using N2 - Advanced Physics Forums
		spherical pendulum using N2 - Advanced Physics Forums
		I'm trying to solve the spherical pendulum using newton's laws, but am coming up with something different than that obtained using the lagrangian formalism.
		The two forces acting on the point mass are the tension $T$ and the gravitational force $mg$, which (in the case where it's moving in a circle of constant \theta) should conspire to produce the centripetal force necessary to keep it in circular motion.
	www.advancedphysics.org /forum/showthread.php?t=2627 (200 words)

	The Complex Geometry of the Spherical Pendulum (ResearchIndex) (Site not responding. Last check: 2007-09-29)
		Abstract: this paper we consider the complexified spherical pendulum.
		For background on the classical spherical pendulum we refer the reader to [?, chpt.
		Following the variation of the period lattice around a closed loop in the complement of the discriminant locus \Delta of a family of elliptic curves (see...
	citeseer.ist.psu.edu /381757.html (339 words)

	Vision Shop - Divination
		Complete with a chart for divination and instruction leaflet, this pendulum is especially designed for questions of love.
		Complette with a divinatory chart and a life management chart, this pendulum is your oracle of answers!
		Specifically designed for question related to wealth and perfect for divining for metallic objects, this pendulum is perfectly weighted and comes with instructions.
	www.visionmagazine.uk.com /VisionShopDivination.htm (503 words)

	[No title] (Site not responding. Last check: 2007-09-29)
		Abstract: Symplectic geometry has its origins in classical mechanics but most modern techniques are heavily influenced by complex algebraic geometry.
		With both the origins and the modern techniques in mind, I will use the spherical pendulum to illustrate physically some of the topology involved in the mirror symmetry of K3 surfaces, examples of which are hypersurfaces given by an equation of degree four.
		Specifically, the set of positions and velocities (or linear momenta) of a spherical pendulum (its phase space) breaks up into subsets with fixed energy and fixed angular momentum.
	www.math.psu.edu /oldColloquium/040916.html (205 words)

	Concerning the nonlinear behaviour of the forced spherical pendulum including the dowsing pendulum
		A spherical pendulum whose support is oscillated sinusoidally in a straight horizontal line will, close to resonance, develop a component of motion transverse to the driver plane.
		The physics of this phenomenon is discussed, supplemented by observations of transverse motion and by measurements of resonance curves for motion constrained to the driver plane.
		The study of the mechanically forced pendulum provides useful insight into the centuries-old problem concerning the dynamics of the hand-forced pendulum as employed by dowsers.
	stacks.iop.org /0143-0807/11/107 (262 words)

	The Driven Pendulum
		The driven pendulum is a simple pendulum whose pivot oscillates with amplitude A and frequency v.
		As with the Double Pendulum and the Spherical Pendulum, we use Lagrange's equations to equation of motion for this pendulum.
		Also, you can alternate between either the vertically driven or horizontally driven pendulums, and turn the oscillations on/off.
	www.maths.surrey.ac.uk /interactivemaths/michaelspages/Driven.htm (132 words)

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