Physics Batch 01 - Classical Mechanics - Programming Framework Analysis
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.
1. Newtonian Dynamics Process
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
Triggers & Inputs
Newtonian Methods
Dynamics Operations
Intermediates
Products
Figure 1. 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.
2. Lagrangian Mechanics Process
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
Triggers & Inputs
Lagrangian Methods
Variational Operations
Intermediates
Products
Figure 2. 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.
3. Hamiltonian Mechanics Process
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
Triggers & Inputs
Hamiltonian Methods
Canonical Operations
Intermediates
Products
Figure 3. 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.