Hamilton's principle
View article: On the Constant (Ratio) \texorpdfstring{$\varepsilon_0 = \gamma/\phi$}{}:\\Existence, Causality, and the Status of the Variational Principle
On the Constant (Ratio) \texorpdfstring{$\varepsilon_0 = \gamma/\phi$}{}:\\Existence, Causality, and the Status of the Variational Principle Open
View article: On the Constant (Ratio) \texorpdfstring{$\varepsilon_0 = \gamma/\phi$}{}:\\Existence, Causality, and the Status of the Variational Principle
On the Constant (Ratio) \texorpdfstring{$\varepsilon_0 = \gamma/\phi$}{}:\\Existence, Causality, and the Status of the Variational Principle Open
View article: 2025-11-16_RFT_The_Relational_Variational_Principle_Why_Omega_Equals_Omega_of_Rc_Is_the_Only_Consistent_Action
2025-11-16_RFT_The_Relational_Variational_Principle_Why_Omega_Equals_Omega_of_Rc_Is_the_Only_Consistent_Action Open
We show that the self-referential identity Ω = Ω[Rc] is not an ansatz but the unique solution to any variational principle in which a system defines its own domain of evaluation. Beginning with a minimal action Srel[Rc, Ω] constrained only…
View article: Spiral Stability Principle v2 (SSP²): Multiscale Stability Equations for Spiral Systems
Spiral Stability Principle v2 (SSP²): Multiscale Stability Equations for Spiral Systems Open
SSP² extends the Spiral Stability Principle to multi-scale biological, physical and computational systems.It introduces cross-domain stability equations for unified modeling.
View article: Contact-Abnormal Geodesics: A New Variational Calculus
Contact-Abnormal Geodesics: A New Variational Calculus Open
This paper introduces and rigorously develops the concept of "contact-abnormal geodesics" within a novel framework of variational calculus. Traditional geodesic theory, deeply rooted in Riemannian geometry and the classical calculus of var…
View article: Contact-Abnormal Geodesics: A New Variational Calculus
Contact-Abnormal Geodesics: A New Variational Calculus Open
This paper introduces and rigorously develops the concept of "contact-abnormal geodesics" within a novel framework of variational calculus. Traditional geodesic theory, deeply rooted in Riemannian geometry and the classical calculus of var…
View article: Spiral Stability Principle v2 (SSP²): Multiscale Stability Equations for Spiral Systems
Spiral Stability Principle v2 (SSP²): Multiscale Stability Equations for Spiral Systems Open
SSP² extends the Spiral Stability Principle to multi-scale biological, physical and computational systems.It introduces cross-domain stability equations for unified modeling.
View article: Universal Ψ Equation Assessment of Feynman's 1948 Path-Integral Method: Variational Closure Failure, Coherence Violations, and Mathematical Inconsistencies
Universal Ψ Equation Assessment of Feynman's 1948 Path-Integral Method: Variational Closure Failure, Coherence Violations, and Mathematical Inconsistencies Open
This technical report provides a complete variational assessment of Feynman’s 1948 path-integral formulation using the fully closed structure of the Universal Ψ Equation. The analysis shows that the path integral, while historically influe…
View article: Universal Ψ Equation Assessment of Feynman's 1948 Path-Integral Method: Variational Closure Failure, Coherence Violations, and Mathematical Inconsistencies
Universal Ψ Equation Assessment of Feynman's 1948 Path-Integral Method: Variational Closure Failure, Coherence Violations, and Mathematical Inconsistencies Open
This technical report provides a complete variational assessment of Feynman’s 1948 path-integral formulation using the fully closed structure of the Universal Ψ Equation. The analysis shows that the path integral, while historically influe…
View article: Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations
Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations Open
In this manuscript, we extend the Lagrangian formulation of \cite{CI08} for Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is naturally derived from a stochastic Hamilton…
View article: Variational bagging: a robust approach for Bayesian uncertainty quantification
Variational bagging: a robust approach for Bayesian uncertainty quantification Open
Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as co…
View article: Variational bagging: a robust approach for Bayesian uncertainty quantification
Variational bagging: a robust approach for Bayesian uncertainty quantification Open
Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as co…
View article: Three-Dimentionality As A First Principle of Hamiltonian Mechanics
Three-Dimentionality As A First Principle of Hamiltonian Mechanics Open
Hamiltonian Mechanics
View article: Three-Dimentionality As A First Principle of Hamiltonian Mechanics
Three-Dimentionality As A First Principle of Hamiltonian Mechanics Open
Hamiltonian Mechanics
View article: The Prince Wave Equation: A Complete Derivation from de Broglie's Fundamental Principle Without Hamiltonian Formalism
The Prince Wave Equation: A Complete Derivation from de Broglie's Fundamental Principle Without Hamiltonian Formalism Open
We derive a complete wave equation framework from de Broglie’s fundamenta relation λ = h/p, expressed in differential form as δp = hδψ where ψ = 1/λ represents spatial compaction. Without invoking Hamiltonian formalism or particle concepts…
View article: The Prince Wave Equation: A Complete Derivation from de Broglie's Fundamental Principle Without Hamiltonian Formalism
The Prince Wave Equation: A Complete Derivation from de Broglie's Fundamental Principle Without Hamiltonian Formalism Open
We derive a complete wave equation framework from de Broglie’s fundamenta relation λ = h/p, expressed in differential form as δp = hδψ where ψ = 1/λ represents spatial compaction. Without invoking Hamiltonian formalism or particle concepts…
View article: Neural optimization of the most probable paths of 3D active Brownian particles
Neural optimization of the most probable paths of 3D active Brownian particles Open
We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup var…
View article: Neural optimization of the most probable paths of 3D active Brownian particles
Neural optimization of the most probable paths of 3D active Brownian particles Open
We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup var…
View article: Geometric integrators for adiabatically closed simple thermodynamic systems
Geometric integrators for adiabatically closed simple thermodynamic systems Open
A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework f…
View article: Geometric integrators for adiabatically closed simple thermodynamic systems
Geometric integrators for adiabatically closed simple thermodynamic systems Open
A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework f…
View article: Thermo-electromechanical nonlinear dynamic response of PZT-4/PZT-5H bidirectional functionally graded porous plates subjected to the variable external harmonic load
Thermo-electromechanical nonlinear dynamic response of PZT-4/PZT-5H bidirectional functionally graded porous plates subjected to the variable external harmonic load Open
This study investigates nonlinear free and forced vibration analysis of bidirectional functionally graded porous (BDFGP) PZT-4/PZT-5H plates subjected to combined thermoelectric and electromechanical loading, focusing on the effect of bidi…
View article: Hu–Washizu variational principle in problems of stability of non-thin anisotropic cylindrical shells made of modern composite materials in spatial formulation
Hu–Washizu variational principle in problems of stability of non-thin anisotropic cylindrical shells made of modern composite materials in spatial formulation Open
In this study, the Hu–Washizu variational principle was employed to derive a three-dimensional system of partial differential equations, which governs the stability of an anisotropic body. This system was expressed in the cylindrical coord…
View article: Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry
Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry Open
Overview. This preprint presents PVP (Protiform's Variational Principle), specifying the pair-potential/force laws under Protiform’s fluctuation kernel Kℓ(r)=e−r/ℓ/rK_\ell(r)=e^{-r/\ell}/rKℓ(r)=e−r/ℓ/r and the sign/proportional-constant di…
View article: A Physical Theory based on the Barycenter Frame of Reference II: Principles of Particle Dynamics
A Physical Theory based on the Barycenter Frame of Reference II: Principles of Particle Dynamics Open
This paper extends the field theory of elastic particle fluids based on the barycenter reference frame and constructs the theoretical foundation of new particle dynamics. According to the particle flow field theory, the complete interactio…
View article: Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry
Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry Open
Overview. This preprint presents PVP (Protiform's Variational Principle), specifying the pair-potential/force laws under Protiform’s fluctuation kernel Kℓ(r)=e−r/ℓ/rK_\ell(r)=e^{-r/\ell}/rKℓ(r)=e−r/ℓ/r and the sign/proportional-constant di…
View article: Vacuum as a Field of Action – VFA-II: Part 1. Unified Variational Principle and Generalized Geometries of Action
Vacuum as a Field of Action – VFA-II: Part 1. Unified Variational Principle and Generalized Geometries of Action Open
The work opens the second phase of the Vacuum as a Field of Action (VFA-II) cycle and develops the previously formulated fundamental relationships of the theory: law of conservation of action ∇μ Tμν = 0, action field equation D★F = Jₐ geom…
View article: Vacuum as a Field of Action – VFA-II: Part 1. Unified Variational Principle and Generalized Geometries of Action
Vacuum as a Field of Action – VFA-II: Part 1. Unified Variational Principle and Generalized Geometries of Action Open
The work opens the second phase of the Vacuum as a Field of Action (VFA-II) cycle and develops the previously formulated fundamental relationships of the theory: law of conservation of action ∇μ Tμν = 0, action field equation D★F = Jₐ geom…
View article: A Level Set Topology Optimization Theory Based on Hamilton's Principle
A Level Set Topology Optimization Theory Based on Hamilton's Principle Open
In this article, we propose a unified variational framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton–Jacobi‐based formulations. The key idea is the introdu…
View article: Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle
Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle Open
This study analytically investigates the large-amplitude vibrations of a fluid-conveying piezoelectric pipe supported at both ends and resting on a nonlinear viscoelastic foundation. To enable energy harvesting, two piezoelectric layers wi…
View article: The Influence of Mass on Dynamic Response of Cracked Timoshenko Beam with Restrained End Conditions: The Truncated Theory
The Influence of Mass on Dynamic Response of Cracked Timoshenko Beam with Restrained End Conditions: The Truncated Theory Open
In this paper, the dynamic response of the Timoshenko cracked beam subjected to a mass is investigated. In turn, it is assumed that the beam has its ends restrained with both transverse and rotational elastic springs. Based on an alternati…