Elasticity and Nonlinear Dynamics Step by Step
A lightweight execution-visualization book.
Stress And Area
force-over-area-defines-normal-stress
doubling-force-doubles-stress
doubling-area-halves-stress
Strain And Young Modulus
extension-over-length-defines-strain
stress-over-strain-defines-young-modulus
wrong-strain-rejects-the-modulus
Bars And Shear
bar-extension-uses-e-a-over-l
doubling-extension-doubles-bar-force
shear-modulus-uses-sideways-strain
Bulk Response And Audit
bulk-modulus-turns-volume-strain-into-pressure
smaller-volume-change-lowers-pressure
elasticity-audit-cites-every-source
Relation Cross Scans
Stress Equivalent Pairs Three-Row Scan
Strain Equivalent Pairs Three-Row Scan
Young Quotient Three-Row Scan
Bar Stiffness Force Three-Row Scan
Shear Modulus Three-Row Scan
Bulk Pressure Ratio Three-Row Scan
Deeper Elasticity Closure Scans
Stress Area Force Inversion Three-Row Scan
Strain Length Extension Inversion Three-Row Scan
Young Stress Force Closure Three-Row Scan
Bulk Pressure Volume Inversion Three-Row Scan
Iteration Ledgers
Affine Map Keeps a Finite Ledger
Quadratic Map Stops Before Denominators Grow
Piecewise Map Records the Branch
Fixed Points and Local Stability
Fixed-Point Substitution Closes the Loop
Slope Less Than One Is a Local Contract
Slope Greater Than One Is Rejected
Period Snapshots
Two-Cycle Must Return and Not Stop
Fixed Point Cannot Spoof a Two-Cycle
Parameter Rows Are Finite Snapshots
Feedback Geometry and Final Audit
Saturating Feedback Checks the Branch
Cobweb Geometry Uses Ledger Points
Dynamics Audit Cites Every Source
Relation Cross-Scans
Fixed Candidate Substitution Cross-Scan
Stability Slope Threshold Cross-Scan
Iteration Depth Error Cross-Scan
Reflection Parameter Period Cross-Scan
Boundary Depth Scans
Logistic Fixed Residual Zero Scan
Stability Margin Boundary Scan
Tent Branch Boundary Scan
Saturating Clamp Boundary Scan
Reflection Return Gap Period Scan
Real Chaos Ledger
Nearby Double Pendulums Diverge Into Chaos