LINE INTEGRALS FOR DIFFERENTIAL EQUATIONS AND LAGRANGIAN

Author Mircea Orasanu

ABSTRACT

We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time. Find out more They determine the observable uncertainties (variances) Δxij of the conjugated components of the position tensor rr of the complex system entity. Thus, one finds from Equation (38) the relation:

1 INTRODUCTION

According to Nottale’s works [6,7] and the previous Relations (36) and (37), the momentum stresses pipj, Equation (35), are generated by unobservable (first term) and observable (second term) stressesFor motions of complex system entities on Peano’s curves at the Compton scale, the uncertainty relations for the diagonal components, Equation (42), are formally similar to those of wave mechanics for the conjugate variables of momentum and position.

The application of the (fractal hydrodynamic) uncertainty relations to concrete complex systems and the evaluation of the state function are demonstrated in the following example. Using the solution for the test particle in the spherically symmetric Coulomb or Newton fields together with the method from where a are specific Coulomb’s or Newton’s lengths and n, l are the standard quantum numbers (n is the principal quantum number and l is the orbital quantum numbers).

According to our previous relations, for the r components of the dynamical variables of the test particle in the spherically symmetric Coulomb or Newton field. these appear in THESIS ( TEZA Author Horia Orasanu )

Dinamica Lagrangiană este capabilă sa opereze cu constrangeri dependente de timp, constrangeri care efectueaza lucru mecanic real, insa nu si lucru mecanic virtual. Ne putem gandi la lucrul mec. virtual ca “un lucru mecanic care a uitat de timp”. Nu exista nici o diferenta intre cele doua tipuri de lucru mecanic atat timp cat se opereaza cu constrangeri dependente de timp. De asemenea in cazul in care caracteristicile materialelor sau ale punctelor materiale si ale

Solidelor pe langa faptul ca sunt positive ,fara sa fie posibile deplasari in cadrul unui solid pe

Rmit optimizari cu legaturi neolonome in vadrul corpului sau solidului

Un caz important al optimizarii legaturilor neolonome este acela al structurilor unde in calculi apar alca

Tuiri din materiale cu proprietatea vasco elastic corespunzatoare anumitor situatiiFurthermore, in the case of narrow entrances that are inaccessible to the robot, the dilation of the walls closes those entrances, diminishes the wave expansion area, and as a consequence reduces the computation time. In this way, the remaining poses define the three-dimensional free configuration space. This step is computed n times, n being the amount of different orientations of the robot for which the C-space is created. The larger value of n that is chosen, the smoother the trajectory that will be computed, since the step in between orientations will be smaller. At the same time, the larger the value of n, the greater the amount of computation time that is needed for this step. An example of the output of this step can be seen in Figure 2, in which the third dimension is the orientation of the robot and n =20. The orientations are repeated above and below the calculated values in order to permit manoeuvres.

References

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MITTAG LEFFLER THEOREM AND FUNCTION AND LAGRANGIAN

Author Horia Orasanu

ABSTRACT

We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any timeIn the context gravity, this may seem a somewhat academic question since nobody has ever experimentally observed a scalar term in the Schrödinger equation of gravitating matter, for a point particle in a curved space, even if torsion is neglected, and it is not even clear, whether gravity will generate torsion outside spinning matter. In other contexts, however, the problem is not so far from physical reality.

INTRODUCTION

. There exist a number of systems which can be described in different ways, often gaining enormously in simplicity by such redescriptions. A common example is the Hamilton operator of a free particle in euclidean space parametrized in terms of spherical coordinates. The operator turns into the Laplace-Beltrami operator.

Unfortunately, the use such reparametrizations is limited. Since they do not change the geometry of the system, they are incapble of teaching us what physics to expect in a space with more complicated geometries.

There exists, however, an important field in physics where relations between different geomentries have been established successfully for a long time. and here we consider parts of THESIS ( TEZA ) Author Horia Orasanu

CAP. 1. Introducere În mecanică, prin ecuațiile lui Hamilton, sau simplu prin Hamiltonian, se înțelege o reformulare a mecanicii clasice, introdusă în 1833 de matematicianul irlandez William Rowan Hamilton, care la rândul său provine din ecuațiile lui Lagrange, o reformulare anterioară a mecanicii clasice introdusă de Joseph Louis Lagrange în 1788. Metoda lui Hamilton diferă de metoda lui Lagrange prin faptul că în loc să exprime ecuațiile diferențiale de ordinul doi pe un spațiu n-dimensional (n fiind numărul gradelor de libertate ale sistemului), le exprimă prin ecuații de ordinul întâi pe un spațiu 2n-dimensional, numit spațiul fazelor

Orice funcție reală netedă H pe o mulțime simplectică poate fi folosită pentru definirea unui sistem Hamiltonian.

Cap. 2. Fondul problemei. LAGRANGIAN si DEFINIREA CONSTRANGERILOR

Aici noi consideram ca

Astfel ca problema de mai sus se reduce la o problema importanta avalorilor proprii de

forma

/t = [p ( x) u]-q ( x ) u

cand sunt indeplinite conditiile la limita si initiale de forma

u( )=

aici conditiile initiale si la limita reprezinta legaturile cinematice ale vitezei care sunt ec

hivalente cu legaturile neolonome ale miscarilor enuntate mai sus ,deci cele care fac part

e din dinamica sistemelor de puncte materiale ,sau sisteme de particule fluide.

This is the physics of plasticity and defects [8]. Defects are described mathematically by means of what are called nonholonomic coordinate transformations. In Fig. 1 we show two typical elementary defects in two dimensions which can be generated by such transformations. It has been understood a long time ago that, geometrically, crystals with defects correspond to spaces with curvature and torsion

In the presence of torsion, the quantum equivalence principle predicts a simple Schrödinger equation. No other approach has done this before

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MITTAG LEFFLER THEOREM

Author Mircea Orasanu ]]>