58 citations · 477 across the 49 of their papers we have counts for
12 papers · 1 filter
New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems
Rupam Das, Z. E. Musielak
The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects…
Null Lagrangians and Gauge Functions in Dynamical Systems: Forces and Nonlinearities
L. C. Vestal, Z. E. Musielak
Among different Lagrangians, null Lagrangians are known for having identically zero the Euler-Lagrange equation and, therefore, they have no effects on the resulting equations of m…
General Null Lagrangians and Their Novel Role in Classical Dynamics
Rupam Das, Zdzislaw E. Musielak
A method for constructing general null Lagrangians and their higher harmonics is presented for dynamical systems with one degree of freedom. It is shown that these Lagrangians can…
Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics
A. L. Segovia, L. C. Vestal, Z. E. Musielak
Standard and non-standard Lagrangians that give the same equation of motion are significantly different in their forms, as the latter do not have terms that clearly discernable ene…
Gauge Functions in Classical Mechanics: From Undriven to Driven Dynamical Systems
Z. E. Musielak, L. C. Vestal, B. D. Tran +1
Novel gauge functions are introduced to non-relativistic classical mechanics and used to define forces. The obtained results show that the gauge functions directly affect the energ…
General null Lagrangians, exact gauge functions and forces in Newtonian mechanics
Zdzislaw E. Musielak, Timothy B. Watson
A method to construct general null Lagrangians and their exact gauge functions is developed. The functions are used to define classical forces independently from Newtonian dynamics…
Null Lagrangians and Invariance of Action: Exact Gauge Functions
Z. E. Musielak
Null Lagrangians and their gauge functions are derived for given standard and non-standard Lagrangians. The obtained standard null Lagrangians generalize those previously found but…
Gauge Functions and Galilean Invariance of Lagrangians
Z. E. Musielak, T. B. Watson
A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance…
Lagrangian formalism and Lie group approach for commutative semigroup of differential equations
Zdzislaw Musielak, Niyousha Davachi, Marialis Rosario-Franco
A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate many novel equations. Two independent methods that…
Special Functions of Mathematical Physics: A Unified Lagrangian Formalism
Zdzislaw Musielak, Niyousha Davachi, Marialis Rosario-Franco
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard La…
Generalized Dirac and Klein-Gordon equations for spinor wavefunctions
R. Huegele, Z. E. Musielak, J. L. Fry
A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. Ne…
Fundamental dynamical equations for spinor wave functions. I. Levy-Leblond and Schrodinger equations
R. Huegele, Z. E. Musielak, J. L. Fry
A search for fundamental (Galilean invariant) dynamical equations for two and four-component spinor wave functions is conducted in Galilean space-time. A dynamical equation is cons…