click links in text for more info


Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called Euler nutation. A pure nutation is a movement of a rotational axis such. In spacecraft dynamics, precession is sometimes referred to as nutation. If a top is set at a tilt on a horizontal surface and spun its rotational axis starts precessing about the vertical. After a short interval, the top settles into a motion in which each point on its rotation axis follows a circular path; the vertical force of gravity produces a horizontal torque τ about the point of contact with the surface. However, there is no precession, the top falls straight downward; this gives rise to an imbalance in torques. In falling, the top overshoots the level at which it would precess and oscillates about this level.

This oscillation is called nutation. If the motion is damped, the oscillations will die down; the physics of nutation in tops and gyroscopes can be explored using the model of a heavy symmetrical top with its tip fixed. The effect of friction is ignored; the motion of the top can be described by three Euler angles: the tilt angle θ between the symmetry axis of the top and the vertical. Thus, precession is the change in φ and nutation is the change in θ. If the top has mass M and its center of mass is at a distance l from the pivot point, its gravitational potential relative to the plane of the support is V = M g l cos ⁡. In a coordinate system where the z axis is the axis of symmetry, the top has angular velocities ω1, ω2, ω3 and moments of inertia I1, I2, I3 about the x, y, z axes. Since we are taking a symmetric top, we have I1=I2; the kinetic energy is E r = 1 2 I 1 + 1 2 I 3 ω 3 2. In terms of the Euler angles, this is E r = 1 2 I 1 + 1 2 I 3 2. If the Euler–Lagrange equations are solved for this system, it is found that the motion depends on two constants a and b.

The rate of precession is related to the tilt by ϕ ˙ = b − a cos ⁡ sin 2 ⁡. The tilt is determined by a differential equation for u = cos of the form u ˙ 2 = f where f is a cubic polynomial that depends on parameters a and b as well as constants that are related to the energy and the gravitational torque; the roots of f are cosines of the angles. One of these is not related to a physical angle; the nutation of a planet occurs because the gravitational effects of other bodies cause the speed of its axial precession to vary over time, so that the speed is not constant. English astronomer James Bradley discovered the nutation of Earth's axis in 1728. Nutation subtly changes the axial tilt of Earth with respect to the ecliptic plane, shifting the major circles of latitude that are defined by the Earth's tilt. In the case of Earth, the principal sources of tidal force are the Sun and Moon, which continuously change locat

Albert J. Beveridge

Albert Jeremiah Beveridge was an American historian and US senator from Indiana. He was an intellectual leader of the Progressive Era and a biographer of Chief Justice John Marshall and President Abraham Lincoln. Beveridge was born on October 6, 1862, in Highland County, near Sugar Tree Ridge. Both of his parents, Thomas H. and Frances Parkinson, were of English descent. His childhood was one of hard labor. Securing an education with difficulty, he became a law clerk in Indianapolis. In 1887, he was admitted to the Indiana bar, practiced law in Indianapolis and married Katherine Langsdale. After Katherine's death in 1900, Beveridge married Catherine Eddy in 1907. Beveridge graduated from Indiana Ashbury University in 1885, with a Ph. B. degree. He was a member of Delta Kappa Epsilon fraternity, he was known as a compelling orator, delivering speeches supporting territorial expansion by the US and increasing the power of the federal government. Beveridge entered politics in 1884 by speaking on behalf of presidential candidate James G. Blaine and was prominent in campaigns in that of 1896, when his speeches attracted general attention.

In 1899, Beveridge was appointed to the U. S. Senate as a Republican and served until 1911, he supported Theodore Roosevelt's progressive views and was the keynote speaker at the new Progressive Party convention which nominated Roosevelt for U. S. President in 1912. Beveridge is known as one of the most prominent American imperialists, he supported the annexation of the Philippines and, along with Republican leader Henry Cabot Lodge, campaigned for the construction of a new navy. In 1901, Beveridge became chair of the Senate Committee on Territories, which allowed him to support statehood for Oklahoma. However, he blocked statehood for New Mexico and Arizona because he deemed the territories too sparsely occupied by white people. In his opinion, they contained too many Hispanics and Native Americans, whom he described as intellectually incapable of understanding the concept of self-governance, he celebrated the "white man's burden" as a noble mission, part of God's plan to bring civilization to the entire world: "It is racial....

He has marked the American people as His chosen nation...."After Beveridge's election in 1905 to a second term, he became identified with the reform-minded faction of the Republican Party. He championed national child labor legislation, broke with President William Howard Taft over the Payne–Aldrich Tariff, sponsored the Federal Meat Inspection Act of 1906, adopted in the wake of the publication of Upton Sinclair's The Jungle. Furthermore, Beveridge joined insurgents in supporting postal savings bank legislation and railroad regulations with the Mann–Elkins Act of 1910, he lost his senate seat to John Worth Kern. In 1912, when Roosevelt left the Republican Party to found the short-lived Progressive Party, Beveridge left with him and ran campaigns as that party's Indiana nominee in the 1912 race for governor and the 1914 race for senator, losing both; when the Progressive Party disintegrated, he returned to the Republicans with his political future in tatters. New but would never again hold office.

Another contribution towards his political downfall was the fact he was a great critic of Woodrow Wilson. He encouraged Wilson to take a more interventionist policy with the Mexican Revolution but disliked Wilson's League of Nations, which Beveridge felt would undermine American independence. In the twilight of his life, Beveridge came to repudiate some of the earlier expansion of governmental power that he had championed in his earlier career. In one notable address, delivered before the Sons of the Revolution's annual dinner in June 1923, Beveridge decried the growth of the regulatory state and the proliferation of regulatory bodies and commissions. "America would be better off as a country and Americans happier and more prosperous as a people," he suggested, "if half of our Government boards and commissions were abolished, hundreds of thousands of our Government officials and employees were discharged and two-thirds of our Government regulations and inhibitions were removed." As his political career drew to a close, Beveridge dedicated his time to writing historical literature.

He was a secretary of the American Historical Association. His four-volume set The Life of John Marshall, published in 1916-1919, won Beveridge a Pulitzer Prize for Biography or Autobiography and connected events in John Marshall's life with his rulings on the US Supreme Court. Beveridge spent most of his final years after his 1922 defeat writing a four-volume biography of Abraham Lincoln, only half-finished at his death, posthumously published in 1928 as Abraham Lincoln, 1809-1858, it revealed a complex and imperfect politician. In 1939, the AHA established the Beveridge Award in his memory, through a gift from the widow and from donations from members. There is a famous lost film of Leo Tolstoy made in 1901, a decade before Tolstoy died. American travel lecturer Burton Holmes visited Yasnaya Polyana with Beveridge; as the three men conversed, Holmes filmed Tolstoy with his 60-mm camera. Afterwards, Beveridge's advisers succeeded in having the film destroyed, for fear that documentary evidence of a meeting with the radical Russian author might hurt his chances of running for the presidency.

"In Support of an American Empire" "The Russian Advance" The Young Man and the World at Project Gutenberg. Th

Albert J. Lindberg Airport

Albert J. Lindberg Airport, is a town owned public use airport located 2 miles south of the central business district of Clark Township, a town in Mackinac County, United States. Although most U. S. airports use the same three-letter location identifier for the FAA and IATA, this airport is assigned 5Y1 by the FAA but has no designation from the IATA. Albert J. Lindberg Airport covers an area of 160 acres at an elevation of 760 feet above mean sea level, it has one runway: 9/27 is 3,700 by 60 feet with an asphalt surface. For the 12-month period ending December 31, 2015, the airport had 250 aircraft operations, an average of 21 per month: all general aviation. In December 2017, there was 1 aircraft based at this airport: 1 single-engine. List of airports in Michigan List of airports in Michigan's Upper Peninsula Albert J Lindberg Airport from the Michigan DOT Airport Directory FAA Terminal Procedures for 5Y1, effective February 27, 2020 Resources for this airport: FAA airport information for 5Y1 AirNav airport information for 5Y1 FlightAware airport information and live flight tracker SkyVector aeronautical chart for 5Y1

William Wightman (Canadian politician)

William Hannum Wightman was a Canadian politician. He was a member of the House of Commons of Canada from 1979 to 1980 who represented the east Toronto riding of Scarborough West. Wightman was born in Quebec, he earned a Bachelor's degree at Clarkson University in New York. He served for two years in the RCAF, he earned a Master's degree in Labour Relations from Columbia University. Before and after his election, he served several private-sector companies in senior industrial relations capacities, as a member of the Ontario Labour Relations Board, he died in Prince Edward County, Ontario in February 2017 at the age of 87. In 1979, he ran as the Progressive Conservative candidate in the riding of Scarborough West, he defeated Liberal incumbent Alan Gray Martin by 2,174 votes. He served as a backbench supporter of the short-lived minority government of Joe Clark. Wightman served as Parliamentary Secretary to the Minister of Labour. In 1980, he came in third place behind the winner, Liberal David Weatherhead and runner-up John Paul Harney.

William WightmanParliament of Canada biography

Raphaƫl Alibert

Raphaël Alibert was a French politician. Raphael Alibert was an ardent Roman Catholic someone with strong royalist ideas. One of the most intense followers of Charles Maurras, Alibert was elected to the Chamber of Deputies for the Action Française party. In October 1939 he and Henry Lémery had visited Maréchal Petain to discuss in private the make-up of a possible ministry with him. In the French government's new Cabinet formed on 16 June 1940 he was appointed Under-Secretary of State to the Prime Minister, now Pétain, he was one of the opposition within the Cabinet to removing the government to North Africa after the Armistice with Germany, it is said that he was instrumental in preventing the departure by President Albert Lebrun and Camille Chautemps on 20 June 1940, although General Weygand opposed to a move, had urged Lebrun to remain until the evening. In the event only 30 deputies and just one senator departed. Alibert was responsible for Exposé des motifs, his document forming the basis for the Révolution Nationale, a proposition which the Chamber and Senate adopted on the 9 July 1940.

Contrary to post-war opinions, Otto Abetz, the German Ambassador in Paris, saw that "nothing could have been further from fascism, whether of the Italian or German variety, than the Revolution Nationale". Abetz felt instead that the government at Vichy believed in "reactionary, hierarchical principals" and that its "nationalism was dangerous to the European concept of the New Order"; the following day Pétain signed. The first announced that he himself was taking over the functions of the'French State', in other words that he was becoming'Head of State'; the second gave the Head of both executive and legislative. The third adjourned the Chamber of Deputies and the Senate sine die. Laval remarked that Pétain had been granted more powers than Louis XIV. Pétain, maintained that he never wished to assume the mantle of a Caesar, that he only wanted to serve until a Peace Treaty with Germany had been signed and he could retire. Alibert was made Keeper of the Seals from 12 July 1940 to 27 January 1941, was appointed Minister of Justice in the new Cabinet formed on 13 July 1940, during the time the government was removed to Vichy.

On 22 July he instituted a review of all naturalisations since 1927. This resulted in 15,000 people, including 600 Jews, having their French citizenships revoked and being made stateless. In keeping with the ideals of Action Francaise, he promulgated the law dissolving secret societies on 13 August 1940, aided in this project by other devout Catholics, notably Bernard Fay, administrator of the Bibliothèque Nationale, Robert Vallery-Radot, their task was to root out about 15,000 Masonic dignitaries from public life, as part of an effort by militant right-wing Christians to displace, while taking revenge on, their'secularising' enemies. The new government took a serious anti-semitic position, he promulgated the first Statut des Juifs of October 1940 which excluded Jews from certain Civil Service posts and presaged action against those in the so-called liberal professions; the German Ambassador to France, Otto Abetz, wrote to von Ribbentrop on 8 October 1940 saying that "some ministers, such as Alibert and Bouthillier, are hoping for an eventual restoration of the Bourbons".

By mid-November that year Alibert, Yvres Bouthillier, Paul Baudouin, Marcel Peyrouton, Jean Darlan and General Huntziger were putting pressure upon Pétain to have Pierre Laval dismissed from office, in which they were successful on 13 December. A furious Abetz visited Pétain calling for Laval's reinstatement and the dismissal of the plotters against him, including Alibert, to no avail. However, on 9 February 1941 Alibert and Pierre-Etienne Flandin were both dismissed from the government, "probably as a sop to the Germans". At the end of the war, Alibert fled abroad into hiding, was condemned to death in absentia on 7 March 1947. Living in exile in Belgium, he was given amnesty in 1959, four years before his death from natural causes. Hôtel du Parc. Raphaël Alibert was played by Jean Périmony Louis Darquier de Pellepoix Xavier Vallat

Town Apartments

Town Residences the Town Apartments, is a high-rise apartment building located at 1511 First Street in Downtown Detroit, Michigan. Designed by Wirt C. Rowland, the structure was built in two distinct phases: construction started in 1928 but was soon halted by the Great Depression, the building was left open to the elements for two decades before being completed in 1953, it was listed on the National Register of Historic Places in 2016. The building was constructed to serve as the clubhouse for the Detroit chapter of the National Town and Country Club; the private organization—which changed its name to Pontchartrain Club in the late 1920s—commissioned architect Wirt C. Rowland of Smith, Hinchman & Grylls to design the structure, envisioned to include public spaces, athletic facilities, rooms for overnight stays. Construction began in September 1928, but came abruptly to an end with the advent of the Great Depression: the Pontchartrain Club closed down and the building was left unfinished, with only the exterior walls and roof completed.

The structure sat vacant and open to the elements—no windows had been installed—for more than twenty years. In the early 1950s it was bought by Cleveland investors and converted into apartments: construction began in 1951 and lasted until 1953, when the utterly remodeled building opened under the name Town Apartments. In September 2014, Triton Investment Co. announced its purchase of the building. Triton had acquired Alden Park Towers along East Jefferson; the $5 million, 18-month renovation, completed in spring 2016, included the installation of new heating and cooling systems, updated windows, new kitchens and flooring in the residences. Other upgrades included an on-site laundry room, bicycle storage, a community room and fitness center; the building was renamed Town Residences. The building stands to a total height of 59 metres; the lower portion of the structure is rectangular in plan while the upper floors feature a U-shaped footprint, with a recessed central section flanked by four-story wings and surmounted by an elaborate two-story tower.

The building is constructed of concrete and steel, faced with tan brick, Mankato stone, granite. Although the façades of the building were designed in the Art Deco architectural style, the exterior was remodeled between 1951 and 1953 to reflect the new International Style aesthetic. Much of the elaborate stone decoration was removed, the tall and narrow windows were replaced with wider openings; the 1953 lobby altered, still retains two sets of original fluted columns. Town Residences — Official Website