Capacitor-spring analogy¶

Map an ideal electrical capacitor to a mechanical spring by preserving constitutive integral form, with voltage corresponding to force, current to velocity, charge to displacement, and capacitance to compliance.

Version: v1 · 2026-09-08 · History
Domain-specific #: 3587
Origin domain: systems engineering
Subdomain: electromechanical analogies

Core Idea¶

The capacitor-spring analogy is a formal cross-domain mapping in which capacitor and spring equations share structure under a chosen force-voltage or alternative network analogy. For the force-voltage mapping, V=(1/C)∫I dt corresponds to F=k∫v dt, so C maps to mechanical compliance 1/k, charge to displacement, and electrical to elastic stored energy. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application¶

Capacitor-spring analogy belongs to systems engineering and is useful where the analyst can specify an ideal capacitor model, an ideal massless linear spring model, selected effort and flow variables, stored energy, constitutive equations, and a declared analogy convention, then evaluate one analogy convention is fixed and constitutive equations, power variables, initial conditions, and stored-energy expressions map consistently without mixing force-voltage and force-current correspondences. The scope is broad within that domain but bounded by the need for one analogy convention is fixed and constitutive equations, power variables, initial conditions, and stored-energy expressions map consistently without mixing force-voltage and force-current correspondences. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making one analogy convention is fixed and constitutive equations, power variables, initial conditions, and stored-energy expressions map consistently without mixing force-voltage and force-current correspondences the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Capacitor-spring analogy can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Capacitor-spring analogy. Capacitor-spring analogy compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: an ideal capacitor model, an ideal massless linear spring model, selected effort and flow variables, stored energy, constitutive equations, and a declared analogy convention. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express one analogy convention is fixed and constitutive equations, power variables, initial conditions, and stored-energy expressions map consistently without mixing force-voltage and force-current correspondences independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of systems engineering because they reuse an ideal capacitor model, an ideal massless linear spring model, selected effort and flow variables, stored energy, constitutive equations, and a declared analogy convention, For the force-voltage mapping, V=(1/C)∫I dt corresponds to F=k∫v dt, so C maps to mechanical compliance 1/k, charge to displacement, and electrical to elastic stored energy., and type the carrier, state every parameter and convention in the definition, test that one analogy convention is fixed and constitutive equations, power variables, initial conditions, and stored-energy expressions map consistently without mixing force-voltage and force-current correspondences, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Capacitor-spring analogy Domain-specific

Parents (1) — more general patterns this builds on

Capacitor-spring analogy is a kind of Analogy Prime

The proposed strict upward parent is prime:analogy.

Hierarchy paths (2) — routes to 2 parentless roots

Capacitor-spring analogy → Analogy → Comparison → Self Checking

Show alternative path (1)

Neighborhood in Abstraction Space¶

Capacitor-spring analogy sits in a moderately populated region (54^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Feedback Control & Dynamical Systems (29 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08