Trajectory · Formal Compendium Rev. 4.1
State Spaces, Time Semantics and Limits of Predictability
The formalization branch of the Trajectory & Intercept Lab consolidates terminology, corrects earlier simplifications and distinguishes geometric possibility from causal reachability.
A Formalization Branch, Not a Replacement for the Lab
The compendium classifies different motion regimes using a common control-theory vocabulary. The educational link does not replace individual physical assumptions or their separate examination. Document revision and implemented release remain distinct evidentiary states.
A Time Slice Is Not a Time Interval
A Fixed-Time Reachable Set describes states reachable at a particular instant. A Reach-Tube aggregates such sets over an interval. Conditioning time, evaluation time and terminal time must be distinguished explicitly.
State Space Is Not a Map View
A spatial projection discards state dimensions such as velocity or energy. Repeated spatial overlap therefore does not mean the full dynamic state remains unchanged. Shape and extent are always tied to the respective modeling assumptions.
Constraints Do Not Automatically Change Dynamics
Narrowing the admissible terminal-state space does not automatically turn a controllable system into a passive ballistic system. Constraints restrict solutions; they do not replace the equations of motion producing them.
Possibility, Causality and Uncertainty
Geometric overlap, temporal compatibility, a retrospectively fitting trajectory and a robust causal strategy are different claims. Nor does a real observation automatically provide full knowledge of future inputs. Probabilities require a separate stochastic model.
Documented Corrections and Open Boundaries
The revision clarifies time indices, spatial projections and the distinction between energy constraints and energy conservation, among other matters. Open issues include complete dynamic formulations, observation models, wind disturbances and a complete differential-game solution. This summary does not prove that all these changes are implemented in the frozen browser lab.