Blog posts
Dual Variational Principles for Curl Forces
Arash Yavari Amit Acharya
Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equations of motion do not, in general, follow from a standard variational principle. In this paper, we present a dual variational formulation for particle dynamics under curl forces. By introducing variables dual to position and velocity and an auxiliary function, we construct a pre-dual action in which the equations of motion act as constraints. Stationarity with respect to the primal variables defines a dual-to-primal mapping, whose substitution into the pre-dual action gives an action expressed entirely in terms of the dual variables. The EulerโLagrange equations of the dual action recover both the original equations of motion and their prescribed initial conditions. We also introduce an auxiliary dual Hamiltonian that is conserved along stationary dual trajectories, although it does not represent the physical energy. The formulation is illustrated using two nonlinear curl force fields in two and three dimensions and the classical Ziegler column. These examples demonstrate that non-conservative curl-force dynamics can admit variational descriptions even in the absence of an ordinary potential energy or a conventional Lagrangian.
๐๐ฎ๐น๐น ๐ณ๐ผ๐ฟ ๐๐ผ๐ป๐๐ฟ๐ถ๐ฏ๐๐๐ถ๐ผ๐ป๐ โ ๐๐๐ก๐๐๐ ๐ฎ๐ฌ๐ฎ๐ฒ ๐ฆ๐๐บ๐ฝ๐ผ๐๐ถ๐๐บ
The ๐ฒ๐
๐๐ฒ๐ป๐ฑ๐ฒ๐ฑ ๐ฎ๐ฏ๐๐๐ฟ๐ฎ๐ฐ๐ ๐๐๐ฏ๐บ๐ถ๐๐๐ถ๐ผ๐ป ๐ฑ๐ฒ๐ฎ๐ฑ๐น๐ถ๐ป๐ฒ ๐ถ๐ ๐ฎ๐ฝ๐ฝ๐ฟ๐ผ๐ฎ๐ฐ๐ต๐ถ๐ป๐ด!
We are pleased to invite researchers to contribute to our symposium at ๐๐๐ก๐๐๐ ๐ฎ๐ฌ๐ฎ๐ฒ (๐ญ๐ฑโ๐ฎ๐ญ ๐ฆ๐ฒ๐ฝ๐๐ฒ๐บ๐ฏ๐ฒ๐ฟ ๐ฎ๐ฌ๐ฎ๐ฒ, ๐๐ฒ๐ฟ๐ฎ๐ธ๐น๐ถ๐ผ๐ป, ๐๐ฟ๐ฒ๐ฒ๐ฐ๐ฒ):
๐ฃ๐ต๐๐๐ถ๐ฐ๐-๐๐ป๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฑ ๐ ๐ฎ๐ฐ๐ต๐ถ๐ป๐ฒ ๐๐ฒ๐ฎ๐ฟ๐ป๐ถ๐ป๐ด ๐ณ๐ผ๐ฟ ๐ก๐๐บ๐ฒ๐ฟ๐ถ๐ฐ๐ฎ๐น ๐๐ป๐ฎ๐น๐๐๐ถ๐ ๐ผ๐ณ ๐ ๐ฒ๐ฐ๐ต๐ฎ๐ป๐ถ๐ฐ๐ฎ๐น ๐ฎ๐ป๐ฑ ๐ ๐๐น๐๐ถ๐ฝ๐ต๐๐๐ถ๐ฐ๐ ๐ฆ๐๐๐๐ฒ๐บ๐
This symposium aims to bring together researchers working at the intersection of ๐๐ฐ๐ถ๐ฒ๐ป๐๐ถ๐ณ๐ถ๐ฐ ๐บ๐ฎ๐ฐ๐ต๐ถ๐ป๐ฒ ๐น๐ฒ๐ฎ๐ฟ๐ป๐ถ๐ป๐ด and ๐ฐ๐ผ๐บ๐ฝ๐๐๐ฎ๐๐ถ๐ผ๐ป๐ฎ๐น ๐บ๐ฒ๐ฐ๐ต๐ฎ๐ป๐ถ๐ฐ๐, with particular emphasis on the development and application of data-driven methods for solving engineering and multiphysics problems.
Thermoelastic anisotropy of lithium niobate from molecular dynamics with a machine-learned interatomic potential
Our latest paper is now freely accessible for the next 50 days from this link: https://authors.elsevier.com/a/1nUCG3In-v8hqF
Postdoctoral Fellow in Origami Materials at McGill University
I am seeking a Postdoctoral Fellow to work on origami metamaterials in the Architected Metamaterials Group at McGill University (https://pasinigroup.mcgill.ca/).
Open PhD Position โ Spring 2026 โ Georgia Tech
The Daedalus Lab at the Georgia Institute of Technology (D. Guggenheim School of Aerospace Engineering) is recruiting a PhD student for Spring 2027.
Our group works at the intersection of fracture mechanics, experimental mechanics, computational modeling, and artificial intelligence. Current research directions include:
Thermodynamic State Index and Conditional Phase-Space Entropy
Someone asked how "Thermodynamic state index in the Unified Mechanics Theory relates, conceptually or mathematically, to conditional phase-space entropy in finite Hamiltonian systems." I posed the question to Gemini AI. Here is its answer in the attached file.
Paper on MechanicsArxiv by Akshay Pakhare, Naba Karan, and Pradeep Guduru: reading sodium storage in hard carbon through stress
As a theoretician, I usually gravitate more towards papers of that kind, but the recently uploaded paper by Pakhare et. al. on MechanicsArxiv, caught my attention simply because it begs for some theoretical mechanics work to be done.