Identifiable Uniqueness of Impulsively Forced, Inert, and Stabilized Body Trajectories
Abstract
An unusual object in the sky raises two related questions: what kind of object it is and what physical process drives its motion. Departures from a gravity-only trajectory can provide evidence, but the same apparent acceleration may be generated by distinct dynamical mechanisms. We formulate this as an identification problem and establish conditions for identifiable uniqueness among three reference classes: inert dynamics, impulsive forcing, and active stabilization such as a controlled spacecraft. The distinction rests on how each class responds to disturbances. Although different mechanisms can produce similar average trajectories, the specified reference models imply different stochastic responses around those trajectories. We show when these differences uniquely determine the dynamical class from the observed trajectory and when several classes remain observationally compatible.
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BibTeX
@misc{andree2026identifiable,
title = {{Identifiable Uniqueness of Impulsively Forced, Inert, and Stabilized Body Trajectories}},
author = {Bo Pieter Johannes Andrée},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25545},
eprint = {2609.25545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25545},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Identifiable Uniqueness of Impulsively Forced, Inert, and Stabilized Body Trajectories
AU - Bo Pieter Johannes Andrée
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25545
UR - https://arxiv.org/abs/2609.25545
AB - An unusual object in the sky raises two related questions: what kind of object it is and what physical process drives its motion. Departures from a gravity-only trajectory can provide evidence, but the same apparent acceleration may be generated by distinct dynamical mechanisms. We formulate this as an identification problem and establish conditions for identifiable uniqueness among three reference classes: inert dynamics, impulsive forcing, and active stabilization such as a controlled spacecraft. The distinction rests on how each class responds to disturbances. Although different mechanisms can produce similar average trajectories, the specified reference models imply different stochastic responses around those trajectories. We show when these differences uniquely determine the dynamical class from the observed trajectory and when several classes remain observationally compatible.
ER -