EQUATION REGISTRY

Accumulated duration at variable speed

Integrate along increasing arc length at positive speed; a stationary interval needs a reference process. This explicitly expands the manuscript’s variable-speed instruction.

Theory · FOUNDATIONEquation version 1.0.0

Based on the final manuscript · Chapters 1–2

t=∫SaSbdSv(S)t=\int_{S_a}^{S_b}\frac{\mathrm dS}{v(S)}

Integrate along increasing arc length at positive speed; a stationary interval needs a reference process. This explicitly expands the manuscript’s variable-speed instruction.
Chapter reference: Final consolidated manuscript · Chapter 2, §I.1; explicit website expansion for variable speed, without a manuscript number · ASD-BOOK-ddbade997b45

Source and ID

ASD-WEB-TIME-001 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Adopted source, conditions and previous versions

Final consolidated manuscript · Chapter 2, §I.1; explicit website expansion for variable speed, without a manuscript number

Integrate along increasing arc length at positive speed; a stationary interval needs a reference process. This explicitly expands the manuscript’s variable-speed instruction.

Conditions retained in this adoption

  • Positive speed along the path; stationary intervals use another reference process
  • Distinguish actual frequency f from display calibration f_ref

Source locators: p0557

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

FND-3dde8d8e081d · 第二章 §一.1,PDF 第 2 页(未单列式号);网站展开

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