Mathematical analysis

Inverse

Geometry

Lagrange multiplier

Physics

Luke's variational principle

Mathematics

Mechanics

Mathematical optimization

Equations of motion

Flow (mathematics)

Compressible flow

Variational method

Compressibility

Variational principle

Operating system

Space (punctuation)

Computer science

Cauchy distribution

Hamilton's principle

Fractal

Classical mechanics

Applied mathematics

Fractals

The semi-inverse method is adopted to establish a family of fractal variational principles of the one-dimensional compressible flow under the microgravity condition, and Cauchy–Lagrange integral is successfully derived from the obtained variational formulation. A suitable application of the Lagrange multiplier method is also elucidated.

A FRACTAL VARIATIONAL THEORY FOR ONE-DIMENSIONAL COMPRESSIBLE FLOW IN A MICROGRAVITY SPACE