Conditional Quadratic Reduction and Orientation Response in the Axis Model
Andrew Morton · Public preprint · Conditional dynamical reduction
Tracks how reducing a quadratic action changes its dynamics, orientation response and coupling to sources.
Abstract
A supplied quadratic collective-coordinate action determines a frequency-dependent Schur complement, a static reduced Hessian and a leading kinetic metric. We derive these maps with their action conventions and show that the effective kinetic metric is a positive pullback. Canonical normalization transforms source vertices and probe covectors together with the Hessian. The resulting matrix entries depend on the declared frame; its generalized spectrum and transformed responses provide the invariant content. For an ordered two-dimensional canonical stiffness matrix we give both eigenprojectors, distinguish the static minimum from the maximum, and state the degenerate boundary. A separately supplied canonical-radius constraint yields a local libration frequency from the eigenvalue splitting, subject to the full tangent stability condition. A prescribed constant-rate cone yields an exact finite-window reader identity; its dynamical admissibility and its measurement window are independent conditions. These results organize a conditional interface for the Axis Model. The physical collective-coordinate realization, sector source normalization and gravitational response require originating matching data. No physical precession frequency, vacuum branch or environmental coupling is selected.
Scope
The dynamical results require a supplied action, radius constraint and stable tangent directions. They establish local libration and conditional averaging identities, while physical precession, time scales and probe identification remain to be established.
Paper and supporting files
The manuscript source and a shared reproducibility package for the conditional calculations are available on Zenodo.
Read the current paper and supporting files on Zenodo