The radial Newton problem: Nonlinear dynamics of minimal resistance in central fields

Rafael López

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: This paper investigates the nonlinear dynamics of Newton’s problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an incompressible source flow. Our analysis reveals that the scale-invariant model suffers from a symmetry-breaking instability (loss of ellipticity) that necessitates geometric truncation. Conversely, we prove that the incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions. These findings provide new qualitative insights into how physical conservation laws ensure the regularity and symmetry of optimal configurations in high-speed central flows, bridging the gap between variational calculus and the physics of complex systems.

Keywords: Newton’s resistance; Radial field; Euler–Lagrange equation; Frustum cone; Rotationally symmetric solution (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008507

DOI: 10.1016/j.chaos.2026.118709

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