Related papers: Nonholonomic constrains: why does not the least ac…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
Cellular development follows a stochastic yet rule-governed trajectory, though the underlying principles remain elusive. Here, we propose that cellular development follows paths of least action, aligning with foundational physical laws that…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
We consider tracking control for multibody systems which are modelled using holonomic and nonholonomic constraints. Furthermore, the systems may be underactuated and contain kinematic loops and are thus described by a set of…
While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model…
The classical relativistic least action principle is revisited from the vacuum field theory approach. New physically motivated versions of relativistic Lorentz type forces are derived, a new relativistic hadronic string model is proposed…
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
The law of action-reaction is thoroughly used in textbooks to derive the conservation laws of linear and angular momentum, and it was considered by Ernst Mach the the cornerstone of physics. We give here a background survey of several…
As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…
Laws of motion given in terms of differential equations can not always be derived from an action principle, at least not without introducing auxiliary variables. By allowing auxiliary variables, e.g. in the form of Lagrange multipliers, an…
The open relativistic two-body problem, when two interacting particles also are in external potentials, is considered in terms of the principle of the least action. Based on the consistent modification of the relativistic version Newton's…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
The Fermat principle indicates that light chooses the temporally shortest path. The action for this "motion" is the observed time, and it has no Lorentz invariance. In this paper we show how this action can be obtained from relativistic…
This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive,…
The law of action-reaction, considered by Ernst Mach the cornerstone of physics, is thoroughly used to derive the conservation laws of linear and angular momentum. However, the conflict between momentum conservation law and Newton's third…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely on each interval of monotonicity, but branching…
The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the…