A streamline of a vector field F is the path of a particle whose velocity is always the arrow beneath it: dx/dt = F(x, y). When F = (∂H/∂y, −∂H/∂x), every streamline lies on a level curve of H: x³ + y³ for (y², −x²), x² + y² for (−y, x), cos x − cos y for (sin y, sin x).

Name: A streamline of a vector field F is the path of a particle whose velocity is always the arrow beneath it: dx/dt = F(x, y). When F = (∂H/∂y, −∂H/∂x), every streamline lies on a level curve of H: x³ + y³ for (y², −x²), x² + y² for (−y, x), cos x − cos y for (sin y, sin x).
Channel: matharium
Description: A streamline of a vector field F is the path of a particle whose velocity is always the arrow beneath it: dx/dt = F(x, y). When F = (∂H/∂y, −∂H/∂x), every streamline lies on a level curve of H: x³ + y³ for (y², −x²), x² + y² for (−y, x), cos x − cos y for (sin y, sin x).

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A streamline of a vector field F is the path of a particle whose velocity is always the arrow beneath it: dx/dt = F(x, y). When F = (∂H/∂y, −∂H/∂x), every streamline lies on a level curve of H: x³ + y³ for (y², −x²), x² + y² for (−y, x), cos x − cos y for (sin y, sin x).

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