Constrained Dynamic Systems
Energy, Reachability, Uncertainty and Evidence
A comparative research synthesis connects Trajectory Lab and Drone/Aerostat through shared questions without equating their models or evidentiary status.
One Research Field, Different Models
Both branches study dynamic systems under energy, control, time and observation constraints. Trajectory examines reachable state sets and observation uncertainty; the A/B branch compares onboard energy from specified initial states. Their connection is an editorial research synthesis, not an executable integration.
Four Independent Questions of Proof
Is the dynamics specified? Does a solution exist, and is it unique? Is the comparison state reachable? Has the numerical method been verified? An energy identity or a single integrated trajectory cannot jointly answer these questions.
Common-Time Viability Is Not MEG
Common-Time Viability tests realizability compatible with time and state constraints. By contrast, the Mission-Equivalence Gate (MEG) defines a shared spatial-kinematic terminal state for two separately considered evolutions. Their arrival times may differ; a MEG proves neither equal total costs nor equivalent missions.
Uncertainty as a Result
Unresolved dynamics, missing measurements and unproven reachability are visible research findings, not gaps to be filled with plausible storytelling. ROS checks sources, assumptions, revisions and conclusions; it replaces neither physics nor empirical testing.
H-A-ATT-01 · Limit of the Reduced State Model
As of the research state of October 18, attitude and rotational dynamics are explicitly recorded as OPEN / NOT_VALIDATED. Translational state determines neither orientation nor stability. Differing stabilization assumptions are comparison assumptions, not a universal consumption law. M1a does not close this modeling boundary.
Reading Path A · System Boundaries and Energy
Drone and Aerostat → Energy and Altitude Gain → M1a Verification. The project branch reconstructs the origins; the baseline defines the comparison; the reference limits the mathematical test core. None of these steps replaces outstanding physical proofs.
Reading Path B · State Spaces and Time
Trajectory & Intercept Lab → Formal Compendium Rev. 4.1 → Cross-Domain Perspectives. The path leads from the educational browser lab to independent formalization and open research hypotheses. Document revision and software freeze are separate.
Reading Path C · ROS and Adversarial Review
ROS Energy Case → Cross-Check of Overall Synthesis → Cross-Domain Perspectives. The new review examines a different research object than the earlier energy audit. The linked graph relationships are thematic and methodological, not production interfaces; FULL_PASS remains NOT_ATTESTED for the synthesis review.