Abstract
We demonstrate that having found a condition for the stationary points in multivariable calculus, that condition may be substituted back into the original equation and still yield the correct stationary points. With that, we emphasise the conditions that must be met in solving multivariable stationary point problems. We further use the analogy of the stationary points problem with finding stationary paths in calculus of variations to apply the latter to circular paths in an axisymmetric potential. Surprisingly, we find that this classical problem does not meet the required conditions. We subsequently derive new conditions that must be met and suggest a possible application.
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