Symmetries for Nonconservative Field Theories on Time Scale

Postavaru, Octavian; Toma, Antonela

doi:10.3390/sym13040552

Cited by 4 publications

(3 citation statements)

References 26 publications

(29 reference statements)

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“…In this section, we establish the criteria for the transformation of Noether symmetries [16,17]. The first observation we make is that, according to Equation (3), we define the generalized nonpotential force…”

Section: Complex Noether Symmetriesmentioning

confidence: 99%

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems

Toma,

Postavaru

2023

Fractal Fract

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Classical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding the stationary values associated with the fractional integral of complex order. The complex Hamiltonian obtained from the Lagrangian is suitable for describing nonconservative systems. We conclude by presenting the conserved quantities attached to Noether symmetries corresponding to complex systems. We illustrate the theory with the aid of the damped oscillatory system.

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Section: Complex Noether Symmetriesmentioning

confidence: 99%

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems

Toma,

Postavaru

2023

Fractal Fract

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“…The statistics of papers called for this Special Issue, related to published or rejected items, are as follows [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]: 26 total submissions, of which 15 were published (57.6%) and 11 rejected (42.3%). The authors geographical distribution is shown in Table 1, and it can be seen that the 38 authors are from 9 different countries.…”

Section: Statistics Of the Special Issuementioning

confidence: 99%

Multibody Systems with Flexible Elements

2021

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“…As the commanding height of science and technology, it greatly enriches the content of attack-defense confrontation in near space [1][2][3][4]. Aiming at the optimal penetration guidance problem of high-speed vehicles against a modified proportional guidance interceptor, this paper obtains the analytical solution of an optimal penetration strategy by introducing Hamilton's principle [5][6][7]. Hamilton's principle is based on the principle of minimum action, which indicates that the motion trajectory of an object in any time interval causes the action to obtain the extreme value.…”

Section: Introductionmentioning

confidence: 99%

Optimal Penetration Guidance Law for High-Speed Vehicles against an Interceptor with Modified Proportional Navigation Guidance

Li¹,

Wang²,

Wang³

et al. 2023

Symmetry

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Aiming at the penetration problem of high-speed vehicles against a modified proportional guidance interceptor, a three-dimensional mathematical model of attack–defense confrontation between the high-speed vehicle and the interceptor is established in this paper. The modified proportional navigation guidance law of the interceptor is included in the model, and control constraints, pitch angle velocity constraints, and dynamic delay are introduced. Then, the performance index of the optimal penetration of high-speed vehicles is established. Under the condition of considering the 180-degree BTT control, the analytical solutions of the optimal speed roll angle and the optimal overload of high-speed vehicles are obtained according to symmetric Hamilton principle. The simulation results show that the overload switching times of high-speed vehicles to achieve optimal penetration are N − 1, where N is the modified proportional guidance coefficient of the interceptor. When the maximum speed roll angle velocity is [60, 90] degrees per second, the penetration effect of high-speed vehicles is good. Finally, the optimal penetration guidance law proposed in this paper can achieve a miss distance of more than 5 m when the overload capacity ratio is 0.33.

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Symmetries for Nonconservative Field Theories on Time Scale

Cited by 4 publications

References 26 publications

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems

Multibody Systems with Flexible Elements

Optimal Penetration Guidance Law for High-Speed Vehicles against an Interceptor with Modified Proportional Navigation Guidance

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