// Use when checking dimensional consistency, estimating physical scales, or deriving functional forms via the Buckingham Pi theorem.
| name | dimensional_analysis |
| description | Use when checking dimensional consistency, estimating physical scales, or deriving functional forms via the Buckingham Pi theorem. |
Apply this skill when you need to verify that equations are dimensionally consistent, estimate the order of magnitude of a physical quantity, or derive the functional dependence of a quantity on relevant parameters without solving the full equations.
Use dimensional reasoning to constrain or derive physical relationships, check equation correctness, and estimate scales.
physical_quantities: The relevant dimensional quantities (masses, lengths, times, charges, etc.)target_quantity: The quantity whose dimensions or functional form you want to determineunit_system: The unit convention in use (SI, natural, CGS, lattice, etc.)dimensional_check: Whether each equation or expression is dimensionally consistent (pass/fail with explanation)pi_groups: Dimensionless combinations identified via Buckingham Pi (if applicable)estimated_scale: Order-of-magnitude estimate of the target quantityMCTS-based autonomous physics problem solver with arXiv search, prior knowledge retrieval, and multi-agent reasoning. Use when you need to solve physics problems, search arXiv for relevant papers, or generate structured physics solutions with iterative refinement.
Use when solving problems involving Maxwell's equations, electrostatics, magnetostatics, electromagnetic waves, radiation, or relativistic electrodynamics.
Use when applying conservation of energy, momentum, angular momentum, charge, or other conserved quantities to constrain or solve a physical system.
Use when decomposing signals or fields into frequency/momentum components, applying Fourier transforms, or using spectral methods to solve differential equations.
Use when solving ordinary or partial differential equations numerically, including choosing integrators, discretization schemes, and stability analysis.
Use when solving a problem by expanding around a known solution in a small parameter, including regular and singular perturbation theory.