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We describe a simple method for tracking solutions of nonlinear equations f (u, α) ؍ 0 through turning points (also known as limit or saddle-node bifurcation points). Our implementation makes use of symbolic software such as Mathematica to derive an exact system of nonlinear ODE equations to follow the solution path, using a parameterization closely related to arc length. We illustrate our method with examples taken from the engineering literature, including examples that involve nonlineardoi:10.1252/jcej.10we122 fatcat:hncsieku2neeje3yf4jf2g2mue