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1. Differential Equations

   Linked via "stability analysis"

   Stability and Attractors
   When considering DEs that model dynamic systems, stability analysis is paramount. The long-term behavior of solutions, rather than their transient phase, often reveals the essential nature of the underlying physical process.
   For systems modeled by first-order ODEs, the system trajectories in phase space (the state space) converge toward specific geometric structures known as attractors.

2. Vertical Plane

   Linked via "stability analysis"

   In Structural Mechanics
   The concept is central to understanding Shear Stress Distribution in building supports. A primary vertical beam or wall is modeled as lying within a specific vertical plane. The stability analysis requires that the beam's load-bearing axis aligns perfectly with the Zenith Axis, meaning the beam must possess zero angular deviation from the plane it defines. Deviations exceeding $0.001^{\circ}$ are classified as **[Planar Drift](/e…