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Rigid body dynamics

Rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body; this excludes bodies that display fluid elastic, plastic behavior. The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law or their derivative form Lagrangian mechanics; the solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems. If a system of particles moves parallel to a fixed plane, the system is said to be constrained to planar movement.

In this case, Newton's laws for a rigid system of N particles, Pi, i=1... N, simplify. Determine the resultant force and torque at a reference point R, to obtain F = ∑ i = 1 N m i A i, T = ∑ i = 1 N ×, where ri denotes the planar trajectory of each particle; the kinematics of a rigid body yields the formula for the acceleration of the particle Pi in terms of the position R and acceleration A of the reference particle as well as the angular velocity vector ω and angular acceleration vector α of the rigid system of particles as, A i = α × + ω × + A. For systems that are constrained to planar movement, the angular velocity and angular acceleration vectors are directed along k perpendicular to the plane of movement, which simplifies this acceleration equation. In this case, the acceleration vectors can be simplified by introducing the unit vectors ei from the reference point R to a point ri and the unit vectors t i = k × e i, so A i = α − ω 2 + A; this yields the resultant force on the system as F = α ∑ i = 1 N m i − ω 2 ∑ i = 1 N m i + A, torque as T = ∑ i = 1 N × = α k → + × A, where e i × e i = 0 and e i × t i = k is the unit

Slo Sco:The Best of the Ballads

Slo Sco: The Best of the Ballads is a compilation album by jazz guitarist John Scofield. The tracks on this album have been taken from released albums on Gramavision Records from 1984 until 1989. "Still Warm" "Heaven Hill" "Phone Home" "True Love" "Time Marches On" "Now She's Blonde" "Spy Versus Spy" "Gil B643" "Thanks Again" "Signature of Venus" "Best Western" "Evansville" John Scofield – guitar David Sanborn – alto saxophone Mitchel Formankeyboards Robert Aries – keyboards Don Grolnick – keyboards Pete Levinsynthesizer Hiram Bullock – guitar Anthony Cox – double bass Gary Grainger – bass guitar Darryl Jones – bass guitar Terri Lyne Carringtondrums Dennis Chambers – drums Steve Jordan – drums Omar Hakim – drums Don Aliaspercussion

1937 Edmonton municipal election

The 1937 municipal election was held November 10, 1937 to elect a mayor and six aldermen to sit on Edmonton City Council and five trustees to sit on the public school board, while four trustees were acclaimed to the separate school board. Voters decided three plebiscite questions. There were ten aldermen on city council, but four of the positions were filled: Hugh MacDonald, James Ogilvie, John McCreath, Athelstan Bissett had been elected to two-year terms in 1936 and were still in office. John Wesley Fry had been elected to a two-year term in 1936, but he resigned to run for mayor. There were seven trustees on the public school board, but two of the positions were filled: Izena Ross and Armour Ford had been elected to two-year terms in 1936 and were still in office. Frederick Casselman had been elected to a two-year term in 1936, but had resigned. On the separate school board there were four vacancies, as A J Crowe, J O Pilon, J O'Hara were continuing. There were 24,279 ballots cast out of 51,599 eligible voters, for a voter turnout of 47%.

Bold or Y indicates elected italics indicate incumbent "SS", where data is available, indicates representative for Edmonton's South Side, with a minimum South Side representation instituted after the city of Strathcona, south of the North Saskatchewan River, amalgamated into Edmonton on February 1, 1912. Hugh Currie, Charles Gariepy, John Whelihan and William Wilde were acclaimed. Are you in favour of the Mayor being elected annually by the members of the City Council from their number? Yes - 4,444 No - 18,383 $35,000 for an Airport Hangar Yes - 5,308 No - 1,578 $25,000 for Police Signals Yes - 3,075 No - 3,159 Election History, City of Edmonton: Elections and Census Office

13062 Podarkes

13062 Podarkes, provisional designation 1991 HN, is a mid-sized Jupiter trojan from the Greek camp 29 kilometers in diameter. It was discovered on 19 April 1991, by American astronomer couple Carolyn and Eugene Shoemaker at the Palomar Observatory, California; the dark Jovian asteroid is the principal body of the proposed Podarkes family. It was named after Podarkes from Greek mythology; the orbit of this Trojan asteroid is unstable. It is orbiting in the leading Greek camp at Jupiter's L4 Lagrangian point, 60° ahead of its orbit, it orbits the Sun at a distance of 5.1 -- 5.2 AU once 9 months. Its orbit has an inclination of 8 ° with respect to the ecliptic; the first used precoveries were taken by Spacewatch of the Steward Observatory at Kitt Peak, extending the asteroid's observation arc by just two weeks prior to its discovery. Fernando Roig and Ricardo Gil-Hutton identified Podarkes as the principal body of a small Jovian asteroid family, using the hierarchical clustering method, which looks for groupings of neighboring asteroids based on the smallest distances between them in the proper orbital element space.

According to the astronomers, the Podarkes family belongs to the larger Menelaus clan, an aggregation of Jupiter trojans, composed of several families, similar to the Flora family in the inner asteroid belt. However this family is not included in David Nesvorný's HCM-analysis from 2014. Instead, Podarkes is listed as a non-family asteroid of the Jovian background population on the Asteroids Dynamic Site which based on another analysis by Milani and Knežević; this minor planet is named after the Greek warrior Podarkes from Greek mythology, who took 40 ships to the Trojan War. He is the son of Ares and brother of Protesilaos, after whom the Jupiter trojan, 3540 Protesilaos, is named. Protesilaos was the first Greek to die in the war; the official naming citation was published by the Minor Planet Center on 13 October 2000. According to the survey carried out by the NEOWISE mission of NASA's space-based Wide-field Infrared Survey Explorer, Podarkes measures 28.96 kilometers in diameter, its surface has an albedo of 0.084, while a generic diameter estimate, based on an absolute magnitude of 11.1 and an albedo at 0.05 gives a larger diameter of 40 kilometers.

As of 2018, no rotational lightcurve of Podarkes has been obtained from photometric observations. The body's rotation period and shape remain unknown. Asteroid Lightcurve Database, query form Dictionary of Minor Planet Names, Google books Asteroids and comets rotation curves, CdR – Observatoire de Genève, Raoul Behrend Discovery Circumstances: Numbered Minor Planets - – Minor Planet Center Asteroid 13062 Podarkes at the Small Bodies Data Ferret 13062 Podarkes at AstDyS-2, Asteroids—Dynamic Site Ephemeris · Observation prediction · Orbital info · Proper elements · Observational info 13062 Podarkes at the JPL Small-Body Database Close approach · Discovery · Ephemeris · Orbit diagram · Orbital elements · Physical parameters

William House (trade unionist)

William House was an English trade unionist. House grew up in the West Auckland area of County Durham, he worked for many years as a coal miner, joined the Independent Labour Party. He was elected to Durham County Council as a checkweighman for his pit, he was prominent in the 1892 miners' strike, became known for his public speaking. In 1899, he was chosen as an agent for the Durham Miners' Association, he was elected as the union's President the following year, serving until his death. House stood for the Labour Party at Bishop Auckland for the January and December 1910 general elections, coming within 5% of victory on the second occasion, he stood unsuccessfully in the 1913 Houghton-le-Spring by-election. The following year, he became Vice-President of the Miners' Federation of Great Britain, he was the union's choice to replace John Wilson in the 1915 Mid Durham by-election, but they chose not to stand him, due to the electoral truce during the First World War

Selca, ┼Żelezniki

Selca is a village in the Municipality of Železniki in the Upper Carniola region of Slovenia. It is an old settlement, first mentioned in 973 AD, was the main settlement and center for the entire Selca Valley, named after the village. Only in more recent times did Železniki become the administrative center for the area; the Baroque parish church in Selca is dedicated to Saint Peter. It belongs to the Archdiocese of Ljubljana. A second church, built just outside the village at the cemetery, is dedicated to the Feast of the Cross. Media related to Selca, Železniki at Wikimedia Commons Selca at Geopedia