What is analytical dynamics?
Analytical dynamics is a modern formulation of classical mechanics; It is a branch of physics describing the effects of forces on the movement of physical objects. The basis of this area is the theory of Sira Isaac Newton and the number that has developed for their formulation. Later scientists, such as Joseph-Louis Lagrange and William Rowan Hamilton, generalized the behavior of physical systems using more advanced and descriptive mathematics. This work was important in studying field theories such as electromagnetism and later development of quantum mechanics.
In Newton's physics, the forces of the body move, as if the objects were infinitely small. The rotating objects were processed as if they were rigid or non -formible due to their movement. These prerequisites bring highly accurate approximation of the real world and are a particularly accessible solution using Newton's number. Mathematically, the strength was considered a vector, the amount of concern and the size. The aim was to calculate, due to the initial position and speed of the object, its position in any otherTime in the future.
Analytical dynamics methodology extends the range of Newtonian mechanics by becoming a more abstract description. Its mathematics does not only describe the location of objects, but can also apply to general physical systems. These include field theories such as those describing electromagnetism and general relativity. Each point in the field can be associated, inter alia, with a vector or scalar, a quantity that is only size and not direction. Analytical dynamics generally uses two scalar properties, kinetic and potential energy to analyze movement rather than vectors.
Lagrangian Mechanics, presented at the end of the 18th century, combined Newton's second law, preservation of momentum, with the first law of thermodienamics, energy preservation. This formulation of analytical dynamics is strong and forms the basis of most modern theories. Lagrangian equations reveal all relevant information about the system andThey can be used to describe everything from Newton's mechanics to general relativity.
In 1833, another improvement in analytical dynamics in the form of Hamilton mechanics, which differs from the Lagrangian method in a way that describes the characteristics of the system. The purpose was not to offer a more convenient method of problem solving, but to provide a deeper insight into the nature of complex dynamic systems. In the next generalization, Hamilton equations were later made to describe quantum mechanics and classic. The abstraction necessary to deepen the insight of analytical dynamics has also expanded the extent of its investigation of other areas of science.