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3-Dimensional analogue of a pendulum
In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass m moving without friction on the surface of a
Spherical_pendulum
System configuration relative to another
Cartesian formulation of the dynamics of the double pendulum. For a 3D example, a spherical pendulum with constant length l free to swing in any angular
Generalized_coordinates
Mechanism for regulating the speed of clocks
Rayleigh–Lorentz pendulum Seconds pendulum Simple harmonic motion Spherical pendulum Spring pendulum Torsional pendulum A "small" swing is one in which
Pendulum
Topics referred to by the same term
a pendulum to keep time Pendulum car, an experimental tilting train Foucault pendulum, a pendulum that demonstrates the Earth's rotation Spherical pendulum
Pendulum_(disambiguation)
Type of mobile robot
of mass (i.e., pendulum-driven system), but there exist some other driving mechanisms. In a wider sense, however, the term "spherical robot" may also
Spherical_robot
Formulation of classical mechanics using momenta
that the force equals the negative gradient of potential energy. A spherical pendulum consists of a mass m moving without friction on the surface of a sphere
Hamiltonian_mechanics
Formulation of classical mechanics
}}+r^{2}\sin ^{2}\theta {\ddot {\phi }}=0\,.} Consider the spherical pendulum, a mass m (known as a "pendulum bob") attached to a rigid rod of length l of negligible
Routhian_mechanics
Weight suspended from a rope which swings in a circular or elliptical path
ordinary pendulums and makes both types of pendulums useful for timekeeping. Newton's laws of motion Pendulum Pendulum (mechanics) Spherical pendulum O'Connor
Conical_pendulum
English polymath (1635–1703)
analogues to understand fundamental processes such as the motion of a spherical pendulum and of a ball in a hollow cone, to demonstrate central force due to
Robert_Hooke
Pendulum with center of mass above pivot
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and falls over without additional help. It can be
Inverted_pendulum
Physics experiment demonstrating resonance
behavior of spherical bodies, the Barton's pendulums experiment demonstrates the physical phenomenon of resonance and the response of pendulums to vibration
Barton's_pendulums
theory Wronskian Loewy decomposition Pendulum Inverted pendulum Double pendulum Foucault pendulum Spherical pendulum Kinematics Equation of motion Dynamics
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
Toy consisting of three balls on a string
edu The Astrojax Pendulum gatech.edu Colin Campbell Variable length spherical pendulum gatech.edu "Astrojax Science". astrojax.com. "The History of Astrojax"
Astrojax
Multiple proofs regarding Earth's approximately spherical shape
Observations of Foucault pendulums, popular in science museums around the world, demonstrate both that the world is spherical and that it rotates (not
Empirical evidence for the spherical shape of Earth
Empirical_evidence_for_the_spherical_shape_of_Earth
Mechanism for regulating the speed of clocks
action transfers energy to the clock's timekeeping element (usually a pendulum or balance wheel) to replace the energy lost to friction during its cycle
Escapement
Dutch mathematician (1942–2010)
Cushman, R.; Duistermaat, J. J. (1988). "The quantum mechanical spherical pendulum". Bulletin of the American Mathematical Society. 19 (2): 475–479.
Hans_Duistermaat
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
oscillation of a compound pendulum is obtained from the ratio of the torque imposed by gravity on the mass of the pendulum to the resistance to acceleration
Moment_of_inertia
Dutch mathematician and physicist (1629–1695)
engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician
Christiaan_Huygens
Model of objects in the sky consisting of a framework of rings
are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting of a spherical framework of
Armillary_sphere
Phase of a cycle
applies to every section of the sphere. Thus if the spherical cap defined by the orbit of the pendulum bob has maximum height h {\displaystyle h} at latitude
Geometric_phase
heavens being a physical dome spanning over it. Early arguments for a spherical Earth pointed to various more subtle empirical observations, including
History_of_geodesy
Inertial navigation design principle
Such a pendulum (sometimes called a Schuler pendulum) would have a length equal to the radius of Earth. Consider a simple gravity pendulum, whose length
Schuler_tuning
Type of pendulum invented in the 1950s
"paraconical" or "ball-borne" pendulum is that the pendulum's fulcrum is the changing point of contact between a spherical metal ball and a flat surface
Paraconical_pendulum
Quantum number denoting orbital angular momentum
dimension and so described as "pendulum" orbits, but were not found in nature. In three-dimensions the orbits become spherical without any nodes crossing
Azimuthal_quantum_number
phenomena. As a base unit of length, scientists had favoured the seconds pendulum (a pendulum with a half-period of one second) one century earlier, but this was
History_of_the_metre
Bulgarian mathematician (1949–2026)
(joint with F. A Grünbaum and L. Haine), and "Perturbations of the spherical pendulum and Abelian integrals". He was the head of the Bulgarian National
Emil_Horozov
French physicist (1819–1868)
1819 – 11 February 1868) was a French physicist who invented the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an
Léon_Foucault
Rotation of Earth around its axis
Panthéon in Paris. Because of Earth's rotation under the swinging pendulum, the pendulum's plane of oscillation appears to rotate at a rate depending on latitude
Earth's_rotation
Self-balancing single wheel personal transporter
The control of a unicycle can be considered to be similar to an inverted pendulum. Many electric unicycles have suspension, either operated by air or springs
Electric_unicycle
Size and shape used to model the Earth for geodesy
depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for
Figure_of_the_Earth
Mobile robot design
is a dynamically-stable mobile robot designed to balance on a single spherical wheel (i.e., a ball). Through its single contact point with the ground
Ballbot
Classroom demonstration used to illustrate principles of classical mechanics
equations of motion. Frictionless plane Kater's pendulum – Reversible free swinging pendulum Spherical cow – Humorous concept in scientific models Swinging
Atwood_machine
Experiment measuring the force of gravity (1797–1798)
Cavendish's diagram of his torsion pendulum, seen from above. The pendulum consists of two small spherical lead weights (h, h) hanging from a 6-foot horizontal
Cavendish_experiment
American artist and inventor
invited to TED to show a series of paintings made by a remote-controlled pendulum. Shannon was commissioned by the Grand Palais in Paris to make a movie
Tom_Shannon_(artist)
Simplification of the basic trigonometric functions
(1985), Spherical Astronomy, Cambridge University Press, p. 19, ISBN 0521317797. Baker, Gregory L.; Blackburn, James A. (2005). "Pendulums somewhat simple"
Small-angle_approximation
Genus of flowering plants
range of colors, sometimes with spots of yellow or blue. The fruit is a spherical capsule. The genus name is derived from the Greek word dierama, meaning
Dierama
Surface formed by rotating an ellipse
903 mi) at the poles. The word spheroid originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal
Spheroid
Concept in fluid mechanics
of added mass in 1828 to describe the motion of a pendulum in a fluid. The period of such a pendulum increased relative to its period in a vacuum (even
Added_mass
Hypothesis that inertial and gravitational masses are equivalent
inertial mass might be different concepts. He compared the periods of pendulums composed of different materials and found them to be identical. From this
Equivalence_principle
Equation for the velocity of a body in viscous fluid
law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. It was
Stokes's_law
Unit of mass equal to that of Earth
also be calculated by observing the motion of the Moon or the period of a pendulum at various elevations, although these methods are less precise than observations
Earth_mass
Small ornamental spring-driven clock
Their production was made possible by the miniaturisation of the torsion pendulum and coil spring mechanism by Nuremberg clockmaker Peter Henlein (d. 1542)
Nuremberg_eggs
Projectiles used by airsoft guns
Airsoft pellets (known as BBs) are spherical projectiles used by airsoft guns. Typically made of plastic, they usually measure around 6 mm (0.24 in) in
Airsoft_pellets
Limiting set in dynamical systems
never return to the vicinity of the limit set. For example, the damped pendulum has two invariant points: the point x0 of minimum height and the point
Attractor
Egyptian mathematician (c. 950–1009)
popular accounts claim that the tenth century astronomer Ibn Yunus used a pendulum for time measurement, despite the fact that it has been known for nearly
Ibn_Yunus
French astronomer
unit). While there he also measured the length of a seconds pendulum, that is a pendulum with a half-swing of one second, and found it to be 1.25 lignes
Jean_Richer
Species of maple tree
in Platanus, paired or opposite in Acer) and in their fruit, which are spherical clusters in Platanus and paired samaras (winged fruit) in Acer. The common
Acer_pseudoplatanus
East-West geographic coordinate
next half century transformed it into an accurate measurement tool. The pendulum clock was patented by Christiaan Huygens in 1657 and gave an increase in
Longitude
density, or whose density varies solely with distance from the centre (spherical symmetry), would produce a gravitational field of uniform magnitude at
Gravity_of_Earth
French polymath (1749–1827)
and an angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying
Pierre-Simon_Laplace
Clock used on ships to aid in navigation
were pendulum clocks, but both the rolling of a ship at sea and the up to 0.2% variations in the gravity of Earth made a simple gravity-based pendulum useless
Marine_chronometer
Precession of a gyroscope due to a nearby celestial body's rotation affecting spacetime
Einstein–Thirring–Lense effect. The gravitational field of a spinning spherical body of constant density was studied by Lense and Thirring in 1918, in
Lense–Thirring_precession
Italian physicist and astronomer (1564–1642)
worked in applied science and technology, describing the properties of the pendulum and "hydrostatic balances". He was one of the earliest developers of the
Galileo_Galilei
Laws in physics about force and motion
for many systems near a stable mechanical equilibrium. For example, a pendulum has a stable equilibrium in the vertical position: if motionless there
Newton's_laws_of_motion
Physical constant for the strength of gravity induced by a mass
measurements than pendulum experiments of the "Schiehallion" (deflection) type or "Peruvian" (period as a function of altitude) type. Pendulum experiments still
Gravitational_constant
Concept for a single-wheeled vehicle
direction. The cabin is balanced on top of this assembly using the inverted pendulum principle and an artificial intelligence control system. The driver's seat
Audi_Snook
In 1656, Dutch scientist Christiaan Huygens invented the pendulum clock, with its pendulum marking the seconds. This gave rise to proposals to use its
History_of_the_metric_system
Outward bulge around a planet's equator due to its rotation
than at the poles. In the 17th century, following the invention of the pendulum clock, French scientists found that clocks sent to French Guiana, on the
Equatorial_bulge
Product of a distance and physical quantity
outside that region a 1/r potential may be expressed as a series of spherical harmonics: Φ ( r ) = ∫ ρ ( r ′ ) | r − r ′ | d 3 r ′ = ∑ ℓ = 0 ∞ ∑ m =
Moment_(physics)
Unpowered spherical deep-sea observation submersible lowered on a cable
Greek βαθύς (bathús) 'deep' and σφαῖρα (sphaîra) 'sphere') was a unique spherical deep-sea submersible which was unpowered and lowered into the ocean on
Bathysphere
Tool used to measure projectile speed
paintball gun or BB gun. Benjamin Robins (1707–1751) invented the ballistic pendulum that measures the momentum of the projectile fired by a gun. Dividing the
Gun_chronograph
Strzys, Martin P. (2014). "Bose-Hubbard dimers, Viviani's windows and pendulum dynamics". J. Phys. A: Math. Theor. 47 (8) 085304. arXiv:1308.3569. Bibcode:2014JPhA
Sphere–cylinder_intersection
Record of humanity's attempts to find east-west position on Earth
govern'd by long Pendulum's, go much truer: But then the difference of Gravity in different Latitudes, the lengthening of the Pendulum-rod by heat, and
History_of_longitude
simply as SWARM) is a kinetic art work consisting of six semi-autonomous spherical robots. It was created in 2007 by a group of engineers and artists including
Orb_Swarm
Engine configuration
modified swashplate to produce a spherical design that directly powers an internal electrical generator. The Taurozzi pendulum engine (U.S. patent 6,382,143)
Swing-piston_engine
Deflection of a spinning object moving through a fluid
Tom. "Artillery Swings Like a Pendulum..." in "The Napoleon Series" Steele, Brett D. (1994). "Muskets and Pendulums: Benjamin Robins, Leonhard Euler
Magnus_effect
Theorem about gravity
over the Earth (as it would be if the Earth were a sphere); he took a pendulum clock to Cayenne, French Guiana and found that it lost 2+1⁄2 minutes per
Clairaut's_theorem_(gravity)
German polymath and scholar (1777–1855)
of pendulum than Foucault's one. The oscillations were observed with a reading telescope, with a vertical scale and a mirror fastened at the pendulum. It
Carl_Friedrich_Gauss
Amusement park in Vienna, Austria
flumes, multiple ghost trains, bumper cars, a hall of mirrors, a funhouse, pendulum rides, and various chair swing rides, including the Praterturm, which reaches
Wurstelprater
Powered mechanical device
connect the bodies in the system are perpendicular to this ground plane. A spherical mechanism is a mechanical system in which the bodies move in a way that
Machine
American physicist, inventor and professor (1911–1988)
binocular Optically stabilized camera lens system Nitrogen detection Inertial pendulum optical stabilizer "The Nobel Prize in Physics 1968". Nobel Foundation
Luis_Walter_Alvarez
Clock
make a clock especially for Wells Cathedral. The clock was converted to pendulum and anchor escapement in the 17th century. The original mechanism was installed
Wells_Cathedral_clock
Chinese scientist and statesman (78–139)
projection, a sling suspending the pendulum, an attachment for the sling, and a horizontal bar supporting the pendulum. Wang Zhenduo argued that the technology
Zhang_Heng
quantum pendulum The three-dimensional potentials The rotating system The linear rigid rotor The symmetric top The particle in a spherically symmetric
List of quantum-mechanical systems with analytical solutions
List_of_quantum-mechanical_systems_with_analytical_solutions
Equations that describe the behavior of a physical system
concept, developed by Huygens and Newton. In the swinging of a simple pendulum, Galileo says in Discourses that "every momentum acquired in the descent
Equations_of_motion
Relativistic correction
rotation of the swing plane of Foucault pendulum can be treated as a result of parallel transport of the pendulum in a 2-dimensional sphere of Euclidean
Thomas_precession
Highest velocity attainable by a falling object
(1851). "On the effect of internal friction of fluids on the motion of pendulums". Transactions of the Cambridge Philosophical Society. 9, part ii: 8–106
Terminal_velocity
in 1992. The two contenders and two Gladiators were enclosed in large spherical cages that they had to propel from within. The contenders' task was to
List_of_Gladiators_UK_events
Abstract coordinate system
(Friedmann equations) Lemaître–Tolman Kasner BKL singularity Gödel Milne Spherical: Schwarzschild (interior Tolman–Oppenheimer–Volkoff equation) Reissner–Nordström
Frame_of_reference
Short story by Edgar Allan Poe
#66 (1974) and by Eternity Comics in Edgar Allan Poe: The Pit and the Pendulum and Other Stories #1 in 1988. In 1975, Warren Publishing released a comic
A_Descent_into_the_Maelström
Framework of distances and directions
can be deceived into thinking that they inhabit a plane, rather than a spherical surface. In fact, the scientists cannot in principle determine whether
Space
Curved path of an object around a point
This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. Eventually, the effect
Orbit
French polymath (1588–1648)
pendulums, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum, that is a pendulum whose
Marin_Mersenne
Study of earthquake-resistant structures
stories) in Tokyo, Japan. Friction pendulum bearing Friction pendulum bearing (FPB) is another name of friction pendulum system (FPS). It is based on three
Earthquake_engineering
Concept of absolute rotation
arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity)
Mach's_principle
Ranged weapon to throw projectiles
to fly inertially and ballistically towards the target. By its double-pendulum kinetics, the sling enables stones (or spears) to be thrown much further
Sling_(weapon)
Difference between ideal and observed gravitational acceleration at a location
observatory on the island of Cayenne. Richer was equipped with a highly precise pendulum clock which had been carefully calibrated at Paris before his departure
Gravity_anomaly
Formulation of classical mechanics
position of the pendulum by the angle θ {\displaystyle \theta } from the vertical. The coordinates and velocity components of the pendulum bob are x p e
Lagrangian_mechanics
Property of objects which appear unchanged after a partial rotation
half-line. In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation)
Rotational_symmetry
American astronomer and mathematician (1773–1838)
1820) and a study of the Lissajous figures created by the motion of a pendulum suspended from two points (1815). In 1816, Harvard awarded Nathaniel Bowditch
Nathaniel_Bowditch
Geodetic survey from 1792 to 1798
"seconds pendulum" (a pendulum with a half-period of one second). In 1656, Christiaan Huygens, inspired by Galileo, invented the first pendulum clock which
Arc measurement of Delambre and Méchain
Arc_measurement_of_Delambre_and_Méchain
Measurement of the strength of a gravitational field
for three years before their deorbit in 2015. Kater's pendulum – Gravity measurement with pendulums Kibble balance § Effect of gravity Felix Andries Vening
Gravimetry
Student-built tether satellite
(made of Dyneema) in two controlled stages, in order to release a small, spherical, lightweight reentry capsule called Fotino into a predetermined trajectory
Young_Engineers'_Satellite_2
Imperial dynasty in China (202 BC – 220 AD)
discerned the cardinal direction of distant earthquakes by use of inverted pendulums. The Han dynasty had many conflicts with the Xiongnu, a nomadic confederation
Han_dynasty
Species of legume
General History of Dichlamydeous Plants. It was reclassified as Racosperma pendulum by Leslie Pedley in 1987 then transferred back to genus Acacia in 2014
Acacia_pendula
Theoretical means of transportation
t+\varphi )} , and describes simple harmonic motion such as in a spring or pendulum. In this case r t = R cos g R t {\displaystyle r_{t}=R\cos {\sqrt {\frac
Gravity_train
Classical statement of gravity as force
the square of the distance between their centers of mass. Separated, spherically symmetrical objects attract and are attracted as if all their mass were
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Space Shuttle orbiter (1992–2011)
it, as the vehicle was displayed in the horizontal atop four friction-pendulum seismic isolators to protect it from earthquakes. The shuttle remained
Space_Shuttle_Endeavour
Greek mathematician and physicist (c. 287 – 212 BC)
Time for Science Education: How Teaching the History and Philosophy of Pendulum Motion Can Contribute to Science Literacy. p. 96. "Archimedes – Galileo
Archimedes
United States historic place
Store. The four-sided clock has brass and steel works contained in a spherical cast iron case which consists of three stages. It was listed on the National
Baxter_Clock
SPHERICAL PENDULUM
SPHERICAL PENDULUM
SPHERICAL PENDULUM
Girl/Female
American, British, English
At the Elder Tree
Boy/Male
British, English
From the Wether-sheep Farm
Girl/Female
Tamil
Complete, One
Boy/Male
Australian, Finnish, French, German
Ready for Battle; Noble; Ready
Male
English
Variant spelling of English unisex Mahalah, MAHALA means "disease."Â
Boy/Male
Indian, Kannada
Krishna
Boy/Male
Hindu, Indian
King Cobra
Boy/Male
Muslim
Victory. Triumph.
Male
Scottish
Scottish name derived from Crìosd, CRÌSDEAN means "Christ." Used as a form of English Christopher, meaning "Christ-bearer."
Male
German
Variant form of German Hugubert, HUPPRECHT means "bright heart/mind/spirit."
SPHERICAL PENDULUM
SPHERICAL PENDULUM
SPHERICAL PENDULUM
SPHERICAL PENDULUM
SPHERICAL PENDULUM
a.
Round; spherical; starlike.
a.
Made convex; protuberant in a spherical form.
a.
Spherical.
a.
See Spheroidal.
a.
Having the form of a bunch of grapes; like a cluster of grapes, as a mineral presenting an aggregation of small spherical or spheroidal prominences.
a.
Spherical; orbicular; orblike; circular.
a.
Globular; spherical; orbicular.
a.
Alt. of Schetical
a.
Alt. of Spheric
a.
Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.
adv.
Spherically.
n.
A portion of a spherical or other convex surface.
n.
Freedom from spherical aberration.
a.
Having the form of a globe; spherical.
n.
The eye, as luminous and spherical.
a.
Exactly spherical; globular.
a.
Round; circular; spherical.
n.
A rudimentary form of crystallite, spherical in shape.
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
v. t.
To form into roundness; to make spherical, or spheral; to perfect.