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| <title>Physics Batch 01 - Classical Mechanics - Programming Framework Analysis</title> | |
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| <h1>Physics Batch 01 - Classical Mechanics - Programming Framework Analysis</h1> | |
| <p>This document presents classical mechanics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p> | |
| <h2>1. Newtonian Dynamics Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A1[System Definition] --> B1[Force Analysis] | |
| C1[Mass Distribution] --> D1[Inertia Calculation] | |
| E1[Initial Conditions] --> F1[Boundary Conditions] | |
| B1 --> G1[Newton First Law] | |
| D1 --> H1[Newton Second Law] | |
| F1 --> I1[Newton Third Law] | |
| G1 --> J1[Inertial Reference Frame] | |
| H1 --> K1[Force Equals Mass Times Acceleration] | |
| I1 --> L1[Action Reaction Pairs] | |
| J1 --> M1[Equilibrium Analysis] | |
| K1 --> L1 | |
| L1 --> N1[Momentum Conservation] | |
| M1 --> O1[Static Equilibrium] | |
| N1 --> P1[Angular Momentum] | |
| O1 --> Q1[Newtonian Dynamics Process] | |
| P1 --> R1[Torque Analysis] | |
| Q1 --> S1[Energy Conservation] | |
| R1 --> T1[Newtonian Dynamics Result] | |
| S1 --> U1[Kinetic Energy] | |
| T1 --> V1[Potential Energy] | |
| U1 --> W1[Newtonian Dynamics Output] | |
| V1 --> X1[Newtonian Dynamics Analysis] | |
| W1 --> Y1[Newtonian Dynamics Final Result] | |
| X1 --> Z1[Newtonian Dynamics Analysis Complete] | |
| style A1 fill:#ff6b6b,color:#fff | |
| style C1 fill:#ff6b6b,color:#fff | |
| style E1 fill:#ff6b6b,color:#fff | |
| style B1 fill:#ffd43b,color:#000 | |
| style D1 fill:#ffd43b,color:#000 | |
| style F1 fill:#ffd43b,color:#000 | |
| style G1 fill:#ffd43b,color:#000 | |
| style H1 fill:#ffd43b,color:#000 | |
| style I1 fill:#ffd43b,color:#000 | |
| style J1 fill:#ffd43b,color:#000 | |
| style K1 fill:#ffd43b,color:#000 | |
| style L1 fill:#ffd43b,color:#000 | |
| style M1 fill:#ffd43b,color:#000 | |
| style N1 fill:#ffd43b,color:#000 | |
| style O1 fill:#ffd43b,color:#000 | |
| style P1 fill:#ffd43b,color:#000 | |
| style Q1 fill:#ffd43b,color:#000 | |
| style R1 fill:#ffd43b,color:#000 | |
| style S1 fill:#ffd43b,color:#000 | |
| style T1 fill:#ffd43b,color:#000 | |
| style U1 fill:#ffd43b,color:#000 | |
| style V1 fill:#ffd43b,color:#000 | |
| style W1 fill:#ffd43b,color:#000 | |
| style X1 fill:#ffd43b,color:#000 | |
| style Y1 fill:#ffd43b,color:#000 | |
| style Z1 fill:#ffd43b,color:#000 | |
| style M1 fill:#51cf66,color:#fff | |
| style N1 fill:#51cf66,color:#fff | |
| style O1 fill:#51cf66,color:#fff | |
| style P1 fill:#51cf66,color:#fff | |
| style Q1 fill:#51cf66,color:#fff | |
| style R1 fill:#51cf66,color:#fff | |
| style S1 fill:#51cf66,color:#fff | |
| style T1 fill:#51cf66,color:#fff | |
| style U1 fill:#51cf66,color:#fff | |
| style V1 fill:#51cf66,color:#fff | |
| style W1 fill:#51cf66,color:#fff | |
| style X1 fill:#51cf66,color:#fff | |
| style Y1 fill:#51cf66,color:#fff | |
| style Z1 fill:#51cf66,color:#fff | |
| style Z1 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Newtonian Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Dynamics Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 1.</strong> Newtonian Dynamics Process. This classical mechanics process visualization demonstrates Newton's laws of motion and force analysis. The flowchart shows system definition and initial conditions, Newtonian methods and laws, dynamics operations and energy analysis, intermediate results, and final Newtonian dynamics outputs. | |
| </div> | |
| </div> | |
| <h2>2. Lagrangian Mechanics Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A2[Generalized Coordinates] --> B2[Configuration Space] | |
| C2[Constraint Analysis] --> D2[Virtual Displacement] | |
| E2[Kinetic Energy] --> F2[Potential Energy] | |
| B2 --> G2[Lagrangian Function] | |
| D2 --> H2[Generalized Forces] | |
| F2 --> I2[Conservative Forces] | |
| G2 --> J2[L equals T minus V] | |
| H2 --> K2[Non Conservative Forces] | |
| I2 --> L2[Euler Lagrange Equations] | |
| J2 --> M2[Action Integral] | |
| K2 --> L2 | |
| L2 --> N2[Variational Principle] | |
| M2 --> O2[Principle of Least Action] | |
| N2 --> P2[Generalized Momentum] | |
| O2 --> Q2[Lagrangian Mechanics Process] | |
| P2 --> R2[Canonical Coordinates] | |
| Q2 --> S2[Symmetry Analysis] | |
| R2 --> T2[Lagrangian Mechanics Result] | |
| S2 --> U2[Noether Theorem] | |
| T2 --> V2[Conservation Laws] | |
| U2 --> W2[Lagrangian Mechanics Output] | |
| V2 --> X2[Lagrangian Mechanics Analysis] | |
| W2 --> Y2[Lagrangian Mechanics Final Result] | |
| X2 --> Z2[Lagrangian Mechanics Analysis Complete] | |
| style A2 fill:#ff6b6b,color:#fff | |
| style C2 fill:#ff6b6b,color:#fff | |
| style E2 fill:#ff6b6b,color:#fff | |
| style B2 fill:#ffd43b,color:#000 | |
| style D2 fill:#ffd43b,color:#000 | |
| style F2 fill:#ffd43b,color:#000 | |
| style G2 fill:#ffd43b,color:#000 | |
| style H2 fill:#ffd43b,color:#000 | |
| style I2 fill:#ffd43b,color:#000 | |
| style J2 fill:#ffd43b,color:#000 | |
| style K2 fill:#ffd43b,color:#000 | |
| style L2 fill:#ffd43b,color:#000 | |
| style M2 fill:#ffd43b,color:#000 | |
| style N2 fill:#ffd43b,color:#000 | |
| style O2 fill:#ffd43b,color:#000 | |
| style P2 fill:#ffd43b,color:#000 | |
| style Q2 fill:#ffd43b,color:#000 | |
| style R2 fill:#ffd43b,color:#000 | |
| style S2 fill:#ffd43b,color:#000 | |
| style T2 fill:#ffd43b,color:#000 | |
| style U2 fill:#ffd43b,color:#000 | |
| style V2 fill:#ffd43b,color:#000 | |
| style W2 fill:#ffd43b,color:#000 | |
| style X2 fill:#ffd43b,color:#000 | |
| style Y2 fill:#ffd43b,color:#000 | |
| style Z2 fill:#ffd43b,color:#000 | |
| style M2 fill:#51cf66,color:#fff | |
| style N2 fill:#51cf66,color:#fff | |
| style O2 fill:#51cf66,color:#fff | |
| style P2 fill:#51cf66,color:#fff | |
| style Q2 fill:#51cf66,color:#fff | |
| style R2 fill:#51cf66,color:#fff | |
| style S2 fill:#51cf66,color:#fff | |
| style T2 fill:#51cf66,color:#fff | |
| style U2 fill:#51cf66,color:#fff | |
| style V2 fill:#51cf66,color:#fff | |
| style W2 fill:#51cf66,color:#fff | |
| style X2 fill:#51cf66,color:#fff | |
| style Y2 fill:#51cf66,color:#fff | |
| style Z2 fill:#51cf66,color:#fff | |
| style Z2 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Lagrangian Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Variational Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 2.</strong> Lagrangian Mechanics Process. This classical mechanics process visualization demonstrates variational principles and generalized coordinates. The flowchart shows generalized coordinates and constraint analysis, Lagrangian methods and variational principles, variational operations and symmetry analysis, intermediate results, and final Lagrangian mechanics outputs. | |
| </div> | |
| </div> | |
| <h2>3. Hamiltonian Mechanics Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A3[Phase Space] --> B3[Canonical Variables] | |
| C3[Legendre Transform] --> D3[Hamiltonian Function] | |
| E3[Poisson Brackets] --> F3[Canonical Equations] | |
| B3 --> G3[Position Momentum Pairs] | |
| D3 --> H3[H equals T plus V] | |
| F3 --> I3[Hamilton Equations] | |
| G3 --> J3[Canonical Transformations] | |
| H3 --> K3[Energy Conservation] | |
| I3 --> L3[Phase Space Evolution] | |
| J3 --> M3[Action Angle Variables] | |
| K3 --> L3 | |
| L3 --> N3[Liouville Theorem] | |
| M3 --> O3[Integrable Systems] | |
| N3 --> P3[Phase Space Volume] | |
| O3 --> Q3[Hamiltonian Mechanics Process] | |
| P3 --> R3[Chaotic Dynamics] | |
| Q3 --> S3[Canonical Perturbation Theory] | |
| R3 --> T3[Hamiltonian Mechanics Result] | |
| S3 --> U3[Adiabatic Invariants] | |
| T3 --> V3[Canonical Quantization] | |
| U3 --> W3[Hamiltonian Mechanics Output] | |
| V3 --> X3[Hamiltonian Mechanics Analysis] | |
| W3 --> Y3[Hamiltonian Mechanics Final Result] | |
| X3 --> Z3[Hamiltonian Mechanics Analysis Complete] | |
| style A3 fill:#ff6b6b,color:#fff | |
| style C3 fill:#ff6b6b,color:#fff | |
| style E3 fill:#ff6b6b,color:#fff | |
| style B3 fill:#ffd43b,color:#000 | |
| style D3 fill:#ffd43b,color:#000 | |
| style F3 fill:#ffd43b,color:#000 | |
| style G3 fill:#ffd43b,color:#000 | |
| style H3 fill:#ffd43b,color:#000 | |
| style I3 fill:#ffd43b,color:#000 | |
| style J3 fill:#ffd43b,color:#000 | |
| style K3 fill:#ffd43b,color:#000 | |
| style L3 fill:#ffd43b,color:#000 | |
| style M3 fill:#ffd43b,color:#000 | |
| style N3 fill:#ffd43b,color:#000 | |
| style O3 fill:#ffd43b,color:#000 | |
| style P3 fill:#ffd43b,color:#000 | |
| style Q3 fill:#ffd43b,color:#000 | |
| style R3 fill:#ffd43b,color:#000 | |
| style S3 fill:#ffd43b,color:#000 | |
| style T3 fill:#ffd43b,color:#000 | |
| style U3 fill:#ffd43b,color:#000 | |
| style V3 fill:#ffd43b,color:#000 | |
| style W3 fill:#ffd43b,color:#000 | |
| style X3 fill:#ffd43b,color:#000 | |
| style Y3 fill:#ffd43b,color:#000 | |
| style Z3 fill:#ffd43b,color:#000 | |
| style M3 fill:#51cf66,color:#fff | |
| style N3 fill:#51cf66,color:#fff | |
| style O3 fill:#51cf66,color:#fff | |
| style P3 fill:#51cf66,color:#fff | |
| style Q3 fill:#51cf66,color:#fff | |
| style R3 fill:#51cf66,color:#fff | |
| style S3 fill:#51cf66,color:#fff | |
| style T3 fill:#51cf66,color:#fff | |
| style U3 fill:#51cf66,color:#fff | |
| style V3 fill:#51cf66,color:#fff | |
| style W3 fill:#51cf66,color:#fff | |
| style X3 fill:#51cf66,color:#fff | |
| style Y3 fill:#51cf66,color:#fff | |
| style Z3 fill:#51cf66,color:#fff | |
| style Z3 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Hamiltonian Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Canonical Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 3.</strong> Hamiltonian Mechanics Process. This classical mechanics process visualization demonstrates phase space dynamics and canonical transformations. The flowchart shows phase space and canonical variables, Hamiltonian methods and transformations, canonical operations and perturbation theory, intermediate results, and final Hamiltonian mechanics outputs. | |
| </div> | |
| </div> | |
| <div class="navigation"> | |
| <h3>Navigation</h3> | |
| <div class="nav-links"> | |
| <a href="physics_index.html" class="nav-link">← Back to Physics Index</a> | |
| <a href="physics_batch_02.html" class="nav-link">Next: Electromagnetism →</a> | |
| <a href="index.html" class="nav-link">Programming Framework Home</a> | |
| </div> | |
| </div> | |
| <div class="footer"> | |
| <p><strong>Generated using the Programming Framework methodology</strong></p> | |
| <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p> | |
| <div class="contact-info"> | |
| <p><strong>Gary Welz</strong></p> | |
| <p>Retired Faculty Member</p> | |
| <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p> | |
| <p>Borough of Manhattan Community College, CUNY</p> | |
| <p>CUNY Graduate Center (New Media Lab)</p> | |
| <p>Email: gwelz@jjay.cuny.edu</p> | |
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