Publish in OALib Journal
APC: Only $99
This paper develops an integrating algorithm for fully rheonomous affine constraints and gives theoretical analysis of the algorithm for the completely integrable case. First, some preliminaries on the fully rheonomous affine constraints are shown. Next, an integrating algorithm that calculates independent first integrals is derived. In addition, the existence of an inverse function utilized in the algorithm is investigated. Then, an example is shown in order to evaluate the effectiveness of the proposed method. By using the proposed integrating algorithm, we can easily calculate independent first integrals for given constraints, and hence it can be utilized for various research fields.
This paper presents a complete integrability condition for fully rheonomous affine constraints in terms of the rheonomous bracket. We first define fully rheonomous affine constraints and develop geometric representation for them. Next, the rheonomous bracket is explained and some properties of it are derived. We then investigate a necessary and sufficient condition on complete integrability for the fully rheonomous affine constraints based on the rheonomous bracket as an extension of Frobenius’ theorem. The effectiveness and the availability of the new results are also evaluated via an example.
In this paper,
integrability conditions and an integrating algorithm of fully rheonomous
affine constraints (FRACs) for the partially integrable case are studied.
First, some preliminaries on the FRACs are illustrated. Next, necessary and
sufficient conditions on the partially integrable case for the FRACs are
derived. Then, an integrating algorithm to calculate independent first
integrals of the FRACs for the partially integrable case is derived. Moreover,
the existence of an inverse function utilized in the algorithm is proven. After
that, an example is presented for evaluation of the effectiveness of the
proposed method. As a result, it turns out that the proposed integrating algorithm
can easily calculate independent first integrals for given partially integrable
FRACs, and thus this new algorithm is expected to be applied to various