Nonstandard Null Lagrangians and Gauge Functions for Newtonian Law of Inertia

Musielak, Z. E.

doi:10.3390/physics3040056

Cited by 9 publications

(11 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…where C 1 and C 2 being constants of integration, and v o and a o being specified by the initial conditions for solving the auxiliary differential equation [28]. Both Lagrangians, when substituted into the E-L equation, give the law of inertia.…”

Section: Dissipative Systems With Displacement-dependent Coefficientsmentioning

confidence: 99%

General Null Lagrangians and Their Novel Role in Classical Dynamics

Das¹,

Musielak²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 be used to obtain non-standard Lagrangians, which give equations of motion for the law of inertia and some dissipative dynamical systems. The necessary condition for deriving equations of motion by using null Lagrangians is presented, and it is demonstrated that this condition plays the same role for null Lagrangians as the Euler-Lagrange equation plays for standard and non-standard Lagrangians. The obtained results and their applications establish a novel role of null Lagrangians in classical dynamics.

show abstract

Section: Dissipative Systems With Displacement-dependent Coefficientsmentioning

confidence: 99%

General Null Lagrangians and Their Novel Role in Classical Dynamics

Das¹,

Musielak²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…where g 1 (t), g 2 (t), and g 3 (t) are arbitrary, but at least twice differentiable, scalar functions of time t. By evaluating these functions for the law of inertia, the following non-standard Lagrangian is obtained [30] L…”

Section: Non-standard Lagrangian For the Law Of Inertiamentioning

confidence: 99%

“…with C 1 and C 2 being constants of integration, and v o and a o being specified by the initial conditions for solving the auxiliary differential equation [30]. An interesting result is that this Lagrangian gives the law of inertia, which is conservative, despite being explicitly dependent on time t [31].…”

Section: Non-standard Lagrangian For the Law Of Inertiamentioning

confidence: 99%

“…Since a o and v o are the integration constants for the auxiliary equation [30], and C 1 and C 2 are the constants of integration for the law of inertia, these constants are determined by the intitial conditions to be specified for a physical problem to be solved. However, both the auxiliary equation and the law of inertia are Galilean invariant; thus, the solutions to these equations must also be the same (Galilean invariant) for all Galilean observers.…”

Section: Galilean Invariancementioning

confidence: 99%

“…Most of the previous work was done by using standard null Lagrangians [24,25]. However, more recently the existence of non-standard null Lagrangians (NSNLs) has been demonstrated [30], and the main objective of this Letter is to use these newly introduced NSNLs to define forces in CM, and convert the law of inertia into the second law of dynamics. Moreover, Galilean invariance of the presented results is investigated and the physical implications are discussed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-standard Null Lagrangians and Forces in Classical Mechanics

Segovia¹,

Vestal²,

Musielak³

2022

Preprint

View full text Add to dashboard Cite

Non-standard Lagrangians are a family of Lagrangians with terms that do not have clearly discernable energy-like forms. A special class among these Lagrangians are non-standard null Lagrangians and their gauge functions, which are used to introduce forces to the laws of dynamics. It is shown that the non-standard Lagrangian for the law of inertia is Galilean invariant but the forces resulting from the non-standard null Lagrangian are not Galilean invariant, except special only time-dependent forces.

show abstract