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  • Published on: 15th October 2019
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It is a  fact is that all Lagrange practically   Were not part of an advance process that originally led to equations, and that their obvious forms are usually obtained in custom fashions instead of being strictly derived from the first principles [4]. 7]. We consider   that   Lagrange   Are standards that can be expressed as differences between "kinetic energy terms" and "potential energy terms";   these   Lagrange   May, or not,   Explicitly rely on time through either the exponential factor and the other function, also referred to Basim   Lagrange   Equivalent ES   [8].  Called   All other formats of   Lagrange who   Discussed in this paper "   The Lagrangeans   "Non-normative   [6];   Note that Arnold [9] refers to it as   Lagrange   natural   .   The dynamic systems discussed in this paper are described by   Equations   The normal differential of   Class II with terms derived from the first order (repeated) of the marital and individual forces, and the coefficients vary either in time or in space.   We refer to these systems as "intermittent" because of first-order derived terms (velocity) in their equations of motion [10, 11].   Keep in mind that this general definition includes both   Systems   Non-conservative with the speed (or alien forces) of speed and conservative systems with conditions of quadratic velocity (or higher than the forces).   The latter are also referred to as "dampening" [10] because the resulting motion equations are constant relative to time, which means that the systems are conservative.   Newtonian mechanics are known to be applied to both   Systems   Governorate   And not   governor.   However, the   Mechanics formulas   And non-Hispanic   Limited to conservative systems [1-5].   The validity of the latter is ensured by the natural result of well-known mathematical theories first demonstrated by Bauer [12].   The natural result shows that it is impossible to apply   Formula  Lagrange starts   Hamilton   variable   The linear waste system described in a single equation of motion with fixed coefficients;   This is a problem with the time of the reversal of the principle of action, which does not allow the choice of a particular direction in time [6].   However, Batman [13] found gaps in Bauer's results and built   Lagrange from   Order intermittent systems.   One technique Bateman Is to add to a system under consideration another system that is reflected in a timely manner and creates a negative friction.   This method leads to two equations of motion, and Hamilton gives them a result of strange solutions that must be eliminated [6, 7].   A dramatic adjustment has been made to this method before Dekker [14 ] Who entered   Equations in the first row   They were   Close together   They are complicated to each other and showed how   Merge them to get   A true equation of the second degree.   Technique Bateman Other are looking at  Lagrangian Which explicitly relies on time through the exponential factor and obtain the desired equation of motion by ignoring the term which is dependent on time [6, 7].   The problem with this approach lies in the fact that the resulting momentum and the amaltonian may not be materially meaningful.   A generalized approach has been developed to deal with non - custodial systems   Riewe [15, 16], which he formulated   Mechanics   Lagrange   And Hamilton using fractional derivatives.   Its main results are the possibility of calculating the non-conserving powers of the potential containing fractional derivatives.   After applying the method to many systems [17, 18], it became clear that their broad applications were limited by the complexity of micro calculus.   Another problem with this method is that its equations are not   Normal   , And that the procedure of changing these equations to equations is well defined   [19].   In addition, the method can not be directly used to estimate linear dissociation systems.   In literature the reverse problem is to find   Lagrange   For a certain equation of motion the Helmholtz problem is called, which requires the solution of helmholtz equations [20, 21].   An alternative approach has been developed by   Musielak et al. [22 ], Which presented a general way to derive a model  Lagrangian standard   For a nonlinear dynamic system with a first-class derivative of the second order   And variable   Coefficients in space coordinates.   In this research, method [22] is used to determine the forms of motion equations that contain   Natural Lagrange   .   Another method was developed to determine the equations of motion that can be derived from   Lagrangeans   Non  Standardists   .   There appear to be two general categories of movement equations   Total Lagrange   Normal   The special layer is one of the motion equations with   Lagrangeans   Non-standard  .   An interesting result is that every general chapter has   Also a subset of the animation equations with   Lagrangians Not standard   .   It is derived   Conditions required   Loggers for standard Lagrangeans   And non-standard   A relationship between these two types is introduced   Lagrange   .   Get through   Lagrangians For many dynamic systems and some basic equations of mathematical physics, the methods presented can be applied to a wide range of physical problems.

FCV

Applied mathematics is divided into several different branches including   an account   Differential   FCV . And has many different applications in many fields, including physics and engineering.   Fcv is one of the classic dynamic dynamic systems.   It is difficult to explain classic dynamic and dynamic systems from the standard calculus.   [1, 2].

Describe   Riewe Potential reciprocal systems are represented by fractional derivatives in 1996 [3, 4].   Then use   Dreisigmeyer And Young Theories   Riewe at   Many dynamic systems.  However, some researchers have suggested, following the Rio approach in the field   Specializations   Complex   , They encountered several restrictions [7].

The literature dealing with the FCV Large [10-19];   However, much remains to be done.   Looks like a class FCV One approach to variable partial verbs ( FALVA ), Which was introduced in [20-22].   Lie feature FALVA That partial function has only one partial parameter and is effectively used in many fields of physics ranging from dynamic systems to quantum field theory, astrophysics, and cosmology [23-33]. This approach can be extended to a huge barrier where more Applications in Physics [34-36].   to me FCV Curve FALVA ,   Gained   Lagrangians Non-standard   (National Security Letters) renewed interest in both classical and quantitative dynamic systems.   Its significance dates back to 1984, more precisely to the periphery of Yang-Mills theory, where national security letters are used to describe large space interactions in terms of the probability of classical theory, which are immediately related to the issue of color reservation .  Aran   he claims Lagrance "Abnormal" by Arnold [38 ] It was observed to play an important role in nonlinear differential equations such as the second nonlinear equation Ricati [39]  Differential equation   Nonlinearity   Non   The linear   [40, 41].   It has been observed that these species play an important role in traditional exchange systems [42-47] and quantum field theories [48, 49].   This is an important issue that deserves special attention and more studies.   National security letters may take great forms, logarithms, etc., and may or may not depend on the time presented by the author in [50].   Applications were discussed in [48, 49, 51] where many moderately modified specifications were derived and disseminated at the classical and quantitative levels.

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