PHYSICS-08 · Undergraduate · ENGLISH · PLANNED
Predict, observe a demonstration, draw a model, then test its limits.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Physics | Analytical Mechanics
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Sign in to save this learning pathPractical outcome: Derive and simulate a pendulum model.
Explain generalised coordinates using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain constraints using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain virtual work using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain action using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Use the first concepts from this section. Derive and simulate a pendulum model. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain euler-lagrange equation using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain cyclic coordinates using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain noether's theorem using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Explain small oscillations using a visual and one worked real-world example. Context: Derive and simulate a pendulum model. End with a prediction or check-for-understanding.
Derive and simulate a pendulum model. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Generalised coordinates, Constraints, Virtual work and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare phase-space trajectories of two oscillators.
Explain canonical momentum using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain legendre transform using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain hamilton's equations using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain phase space using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare phase-space trajectories of two oscillators. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain poisson brackets using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain canonical transformations using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain liouville's theorem using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Explain hamilton-jacobi introduction using a visual and one worked real-world example. Context: Compare phase-space trajectories of two oscillators. End with a prediction or check-for-understanding.
Compare phase-space trajectories of two oscillators. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Canonical momentum, Legendre transform, Hamilton's equations and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare regular and chaotic motion using the same numerical settings.
Explain central-force motion using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain effective potentials using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain two-body reduction using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain rigid-body rotation using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare regular and chaotic motion using the same numerical settings. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain euler angles using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain coupled oscillators using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain poincare sections using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Explain lyapunov exponents using a visual and one worked real-world example. Context: Compare regular and chaotic motion using the same numerical settings. End with a prediction or check-for-understanding.
Compare regular and chaotic motion using the same numerical settings. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Central-force motion, Effective potentials, Two-body reduction and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Compare regular and chaotic motion using the same numerical settings. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Analytical Mechanics, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Diagrams, virtual experiments, data analysis and simulations. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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