Kinetic energy and low-speed expansion

Follows from the momentum–work integral without first specifying rest energy.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 2

E_k=m_0c^2(\gamma-1)=\frac{m_0v^2}{2}+\frac{3m_0v^4}{8c^2}+O\!\left(\frac{m_0v^6}{c^4}\right)

Follows from the momentum–work integral without first specifying rest energy.
Chapter reference: Final collected manuscript · Chapter 2 §III.4 (2.23); low-speed series expanded on the website · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Final collected manuscript · Chapter 2 §III.4 (2.23); low-speed series expanded on the website

Follows from the momentum–work integral without first specifying rest energy.

Conditions retained in this adoption

Uniform background, fixed internal state, 0≤v<c and no net radiation.
The LVE directional law and inertial angular weight are separate inputs.
m₀=C_m m_def; adopt C_m=1 and universal mass normalization.

Specific unresolved source issues

The microscopic core profile, inertial weight and four mass responses still require one common structural solution.

Source locators: p0654 · p0656 · p0658 · p0660 · p0661 · p0663 · p0666 · p0936 · 最终合订稿 · 第二章 §三.4 (2.23)；低速级数为网页展开

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

FND-3dde8d8e081d · 第二章 §三，(2.23), PDF p. 9

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