Expert-level statics covering equilibrium of rigid bodies, free body diagrams, trusses, frames, friction, centroids, and moments of inertia.
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Conditions: sum of forces equals zero, sum of moments equals zero. 2D equilibrium: three equations, Fx = 0, Fy = 0, moment about any point = 0. 3D equilibrium: six equations, three force and three moment equations. Free body diagram: isolate body, show all external forces and moments. Support reactions: pin provides two force reactions, roller one, fixed provides all.
Truss: two-force members connected at joints, loads only at joints. Method of joints: sum forces at each joint, two equations per joint. Method of sections: cut through up to three members, sum forces and moments. Zero force members: can be identified by inspection, simplify analysis. Determinacy: m + r = 2j for statically determinate truss.
Coulomb friction: F = mu times N, friction force proportional to normal force. Static vs kinetic: static coefficient larger than kinetic. Impending motion: maximum static friction just before sliding begins. Wedge friction: self-locking condition when friction angle exceeds wedge angle.
Centroid: geometric center, weighted average position of area or volume. Composite bodies: sum of component centroids weighted by area or volume. Second moment of area: I = integral of y squared dA, resists bending. Parallel axis theorem: I = Icm + A times d squared.
| Pitfall | Fix |
|---|---|
| Incomplete free body diagram | Identify and include all contact forces and applied loads |
| Wrong sign convention | Define positive directions clearly at start |
| Ignoring weight of members | Include member weight unless stated massless |
| Moment sign error | Use right-hand rule consistently for 3D problems |
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概要と使いどころ
Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
日本語の概要は準備中です。原文の説明を表示しています。