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The goal and the main result of the paper is to provide a completedescription of the field of rational differential invariants of one class ofsecond order ordinary differential equations with scalar control parameter withrespect to Lie pseudo-group of local feedback transformations. In particular,considered class describes behavior of conservative mechanical systems. Weconstruct the class of rational differential invariants that separate regularorbits. It is well known that differential invariants form algebra with respectto the operation of addition and multiplication. In our case, constructedrational differential operators form a field (in algebraic sense).

Differential invariants of feedback transformations for quasi-harmonic oscillation equations