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Newtonian dynamics

In physics, the Newtonian dynamics is understood as the dynamics of a particle or a small body according to Newton's laws of motion. The Newtonian dynamics occurs in a three-dimensional Euclidean space, flat. However, in mathematics Newton's laws of motion can be generalized to multidimensional and curved spaces; the term Newtonian dynamics is narrowed to Newton's second law m a = F. Consider N particles with masses m 1, …, m N in the regular three-dimensional Euclidean space. Let r 1, …, r N be their radius-vectors in some inertial coordinate system; the motion of these particles is governed by Newton's second law applied to each of them The three-dimensional radius-vectors r 1, …, r N can be built into a single n = 3 N -dimensional radius-vector. Three-dimensional velocity vectors v 1, …, v N can be built into a single n = 3 N -dimensional velocity vector: In terms of the multidimensional vectors the equations are written as i.e. they take the form of Newton's second law applied to a single particle with the unit mass m = 1.

Definition. The equations are called the equations of a Newtonian dynamical system in a flat multidimensional Euclidean space, called the configuration space of this system, its points are marked by the radius-vector r. The space whose points are marked by the pair of vectors is called the phase space of the dynamical system; the configuration space and the phase space of the dynamical system both are Euclidean spaces, i. e. they are equipped with a Euclidean structure. The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass m = 1 is equal to the sum of kinetic energies of the three-dimensional particles with the masses m 1, …, m N: In some cases the motion of the particles with the masses m 1, …, m N can be constrained. Typical constraints look like scalar equations of the form Constraints of the form are called holonomic and scleronomic. In terms of the radius-vector r of the Newtonian dynamical system they are written as Each such constraint reduces by one the number of degrees of freedom of the Newtonian dynamical system.

Therefore, the constrained system has n = 3 N − K degrees of freedom. Definition; the constraint equations define an n -dimensional manifold M within the configuration space of the Newtonian dynamical system. This manifold, its tangent bundle. Let q 1, …, q n be the internal coordinates of a point of M, their usage is typical for the Lagrangian mechanics. The radius-vector r is expressed as some definite function of q 1, …, q n: The vector-function resolves the constraint equations in the sense that upon substituting into the equations are fulfilled identically in q 1, …, q n; the velocity vector of the constrained Newtonian dynamical system is expressed in terms of the partial derivatives of the vector-function: The quantities q ˙ 1, …, q ˙ n are called internal components of the velocity vector. Sometimes they are denoted with the use

Temple of the Dog

Temple of the Dog was an American rock supergroup that formed in Seattle, Washington in 1990. It was conceived by vocalist Chris Cornell of Soundgarden as a tribute to his friend, the late Andrew Wood, lead singer of the bands Malfunkshun and Mother Love Bone; the lineup included Stone Gossard on rhythm guitar, Jeff Ament on bass guitar, Mike McCready on lead guitar, Matt Cameron on drums. Eddie Vedder appeared as a guest to provide some backing vocals; the band released its only album, the self-titled Temple of the Dog, in April 1991 through A&M Records. The recording sessions took place in November and December 1990 at London Bridge Studios in Seattle, with producer Rakesh "Rick" Parashar. Although earning praise from music critics at the time of its release, the album was not recognized until 1992, when Vedder, Gossard, McCready had their breakthrough with Pearl Jam. Cameron would join Pearl Jam, serving as drummer since 1998; the band toured in 2016 in celebration of the 25th anniversary of their self-titled album.

Temple of the Dog was started by Soundgarden frontman Chris Cornell, a roommate of Andrew Wood, the lead singer of Malfunkshun and Mother Love Bone. Wood died on March 1990, of a heroin overdose, the day Cornell got back from a tour; as he went on to tour Europe a few days he started writing songs in tribute to his late friend. The result was two songs, "Reach Down" and "Say Hello 2 Heaven", which he recorded as soon as he returned home from touring; the recorded material was slow and melodic, musically different from the aggressive rock music of Soundgarden. Cornell approached Wood's former bandmates, Stone Gossard and Jeff Ament—who were still figuring out how to continue without Mother Love Bone—with the intention of releasing the songs as a single. Ament described the collaboration as "a good thing at the time" for Gossard and him that put them into a "band situation where we could play and make music." The band's lineup was completed by the addition of Soundgarden drummer Matt Cameron and future Pearl Jam lead guitarist Mike McCready.

They named themselves Temple of the Dog, a reference to a line in the lyrics of the Mother Love Bone song "Man of Golden Words". The band started rehearsing "Reach Down", "Say Hello 2 Heaven", other songs that Cornell had written on tour prior to Wood's death, as well as re-working some existing material from demos written by Gossard and Cameron. One such demo became a song for two bands, recorded as "Footsteps" by Pearl Jam and "Times of Trouble" by Temple of the Dog; the idea of doing covers of Wood's solo material came up but was abandoned as they realized it would make people think the band was "exploiting his material."The release of a single was soon deemed a "stupid idea" by Cornell and dropped in favor of an EP or album. The album was recorded in only 15 days, produced by the band themselves. Gossard described the recording process as a "non-pressure-filled" situation, as there were no expectations or pressure coming from the record company. Eddie Vedder, who had flown up from San Diego to Seattle to audition for Ament, McCready to be the singer of a band billing themselves as Mookie Blaylock, was at one of the Temple of the Dog rehearsals and ended up providing backing vocals.

"Hunger Strike" became a duet between Vedder. Cornell was still figuring out the vocals at practice when Vedder stepped in and filled in the blanks singing the low parts because he saw it was hard for Cornell, as Cornell described it: "He sang half of that song not knowing that I'd wanted the part to be there and he sang it the way I was thinking about doing it, just instinctively." "Hunger Strike" became Temple of the Dog's breakout single. On the 2011 documentary Pearl Jam Twenty, Vedder stated, it could be one of my favorite songs that I’ve been on — or the most meaningful.”Temple of the Dog was released on April 16, 1991, through A&M Records and sold 70,000 copies in the United States. Ament recalled that A&M requested a Pearl Jam sticker be on the cover—as they had just picked their new name—because "it'll be a good thing for us", but they refused; the album failed to chart. Critic Steve Huey of AllMusic rated the album with four-and-a-half stars out of five, stating that the "record sounds like a bridge between Mother Love Bone's theatrical'70s-rock updates and Pearl Jam's hard-rocking seriousness."

David Fricke of Rolling Stone wrote in retrospect that the album "deserves immortality." The band members were pleased with the material. Soon after the album's release and Pearl Jam embarked on recording their next albums, the Temple of the Dog project was brought to a close. In the summer of 1992, the album received new attention. Although it had been released more than a year earlier, A&M Records realized that they had in their catalog what was a collaboration between Soundgarden and Pearl Jam, who had both risen to mainstream attention in the months since the album's release with their respective albums and Ten. A&M decided to reissue the album and promote "Hunger Strike" as a single with an accompanying music video, filmed; the attention allo

Southeast Peninsula (Saint Kitts)

The Southeast Peninsula of Saint Kitts island is located in Saint Kitts and Nevis, in the Lesser Antilles archipelago of the Caribbean. It stretches southeast from the country's capital, for ~14 kilometres to the waters of The Narrows, the strait which separates Saint Kitts island nearby Nevis island, it is connected to the rest of the island by an isthmus which, at its narrowest, is less than one kilometre wide. Features of the peninsula include the Great Salt Pond, the country's largest lake, St. Anthony's Peak, Turtle Beach, several bays; until this scrubby, low-lying peninsula, was less extensively developed than the rest of the island, being accessible by boat. The construction of an all-weather road during the 1990s has led to some development around Turtle Beach


Kyl21 is an ice cream with popsicles in futuristic looking geometric shapes, new textures and gourmet recipes. The science-food-company Molekyleis Produktionsgesellschaft mbH was founded in 2014 by product designer and marketing specialist David Marx in Berlin. David Marx produces flash-frozen ice using his own technology based on liquid nitrogen, which allows popsicles in geometric shapes, new textures and highend recipes; the molekylice is produced at around −200 °C. The molekylice came out of the Science Kitchen - an independent food lab based in Berlin and Singapore that specializes in molecular gastronomy by inventing and developing food products for a sustainable, vegan-friendly future; the Molekylice is produced in Los Angeles and China. The Kyl21 name is a mash-up of the Norwegian word for molecule "molekyl", the age of Marx's intended popsicle audience. Through crowdinvesting at Companisto, Kyl21 was able to collect € 940.650 venture capital. List of ice cream brands Official website


The SS-Ehrendolch was considered an honour weapon of the SS of the Nazi Party. In addition to this dagger there was the SS Honour Ring and SS Honour Sword; the awarding ceremony was conducted according to strict rules developed by Heinrich Himmler. This honour weapon was introduced in December 1933, following analogous traditions in the army, air force and navy; the awarding ceremony took place on November 9, during the final introduction of the SS-men in the Allgemeine SS, SS-Totenkopfverbände units and SS-Verfügungstruppe every year. The SS dagger was an official sidearm of the SS-dress uniform used by all full members of the SS. Production of these honour daggers was suspended in 1940; the design of the weapon was based on the 16th century Swiss dagger. The center of the wide and spear-pointed and 33 cm long blade has a pronounced rib. Along the longer axis of the blade the slogan of the SS "Meine Ehre heißt Treue" was etched; the cross-guard and pommel were nickel-plated. The metal scabbard mount.

The SS dagger was introduced in 1933 and there are three distinctive versions available, depending on the year of manufacturing. Early production: 1933-1935: Manufacturer's logo, black burnished ebony handle, hilt with Roman numerals. On June 21, 1936, another variant of the dagger was introduced, awarded only to those SS officers and NCOs who had joined the SS before 1933; this dagger was identical to the 1933 model, but the scabbard was fitted with a chain made of rectangular plaques adorned with skulls and SS runes and an additional silver fitting with swastika motif. High-ranking SS leaders were presented a special dagger bearing the inscription "In warm camaraderie, H. Himmler". There were numerous variants of this dagger, which were handed to the recipients by Heinrich Himmler; these gift daggers were identical to the general-issue daggers, but were made of top quality materials and had gilded inscriptions. They were and still are considered a rarity due to the low number issued; the SS honour daggers were worn with black SS uniform.

According to Himmler, every SS member was obliged to use the dagger against anyone who had violated the honour of the SS or offended the honour or the family of the SS member. In November 1935, Himmler issued a decree stating that "every SS man has the right and duty to defend his honour with the weapon." As of February 15, 1943 all officers of the Waffen-SS were entitled to wear this dagger with the field-gray dress uniforms. For these occasions, the dagger was fitted with a tassle and sword knot made of aluminium lace, similar to one used by Wehrmacht officers. Gordon Williamson: The Waffen-SS - A Handbook p. 158 Heinz Höhne: The Order of the Death's Head. The history of the SS. Weltbildverlag, 1992, ISBN 3-89350-549-0, p 140 Miller, Michael. Knight's Cross Holders of the SS and German Police 1940-45. England: Helion & Company. ISBN 978-1-909982-74-1


Ghoshpur is a village in Sandeshkhali I CD Block in Basirhat subdivision of North 24 Parganas district in the state of West Bengal, India. As per the 2011 Census of India, Ghoshpur had a total population of 6,606, of which 3,330 were males and 3,276 were females. Population below 6 years was 725; the total number of literates in Ghoshpur was 4,293. Sandeshkhali I CD Block is served by Nazat PS; the CD Block headquarters are located at Nazat, across the Besti River. One can reach Nazat by ferry from Ghoshpur ferry ghat to Boyermari ferryghat at Nazat. Kalinagar Mahavidyalaya at Kalinagar is located nearby. Ghoshpur Rural Hospital at Ghoshpur with 30 beds functions as the main medical facility in Sandeshkhali I CD Block. There are primary health centres at Agarbati and Nazat