\[ S_{0}=\int \sum_{i} p_{i} d q_{i}=\int \sum_{i} a_{i k} d q_{i} d q_{k} / d t \] \[ S_{0}=\int \sum_{i} p_{i} d q_{i}=\int \sum_{i} a_{i k} d q_{i} d q_{k} / d t=\int \sqrt{\left[2(E-V) \sum a_{i k...\[ S_{0}=\int \sum_{i} p_{i} d q_{i}=\int \sum_{i} a_{i k} d q_{i} d q_{k} / d t \] \[ S_{0}=\int \sum_{i} p_{i} d q_{i}=\int \sum_{i} a_{i k} d q_{i} d q_{k} / d t=\int \sqrt{\left[2(E-V) \sum a_{i k} d q_{i} d q_{k}\right]} \] The matrix \(a_{i k}\) sometimes called the mass matrix, is evidently a metric, a measure in the configuration space, by which the “length” of the paths, and particularly the minimum action path, are measured.
