Cover of The Smooth Dance of Two Spheres: An Exact Calculation in Fluid Mechanics

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The Smooth Dance of Two Spheres

An Exact Calculation in Fluid Mechanics

What does it take to calculate something exactly?

Most calculations stop once an approximation is good enough. This book follows one classical problem all the way to an exact result: the hydrodynamic interaction of two spheres in a viscous fluid.

Working through the core ideas of a 1984 paper, Kengo Ichiki moves from Stokes flow to recurrence relations, working C code, arbitrary-precision arithmetic, and tables of exact rational coefficients.

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From approximation to exact results

Follow the problem from equations to code and onward to 1,414 exact coefficient values, while also meeting the people and persistence behind the research.

A finite decimal, 0.333333, giving way to the exact fraction one third

From Approximation to Exact Calculation

Instead of stopping at a "good enough" floating-point approximation, the calculation uses exact rational arithmetic with GMP to obtain exact coefficient values.

A diagram leading from the Stokes equations to C code and a table of coefficients

From Equations to Code and Tables

Follow Stokes flow, Lamb's general solution, and the Jeffrey–Onishi recurrence relations into working C code, then onward to tables containing 1,414 exact coefficient values.

A blurred bookshelf filled with books on fluid mechanics, mathematics, and physics

The Human Story of Research

Meet the mentors and collaborators, the wrong turns and failures, and the passion, struggles, and dogged persistence: the human story that formal papers leave out.

Continue with the code and coefficient tables

The book tells the mathematical and human story of the calculation. The companion twobody resources let you inspect the programs and the resulting exact resistance-function coefficients directly.

Explore the calculations View the C code on GitHub

For curious readers

This is an independently produced technical book for readers who want both the mathematics and the human story behind the research. It opens a door into physics research rarely seen outside academic papers.

Kindle and paperback

The Smooth Dance of Two Spheres: An Exact Calculation in Fluid Mechanics is available in Kindle and paperback editions.

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