The nonlinear simple pendulum is investigated to find the exact closed-form analytical solution, satisfying initial conditions of angular position and angular velocity. While previous numerous studies have been conducted on the nonlinear simple pendulum, the exact closed-form analytical solution still remains not available in public domain for the most general initial condition including initial angular velocity as well as initial angular displacement. In this paper, the exact closed-form analytical solution for the general initial conditions is derived using Jacobi’s elliptic function and elliptic integral. The result was verified by comparing it with previous studies and the numerical solution of the equation of motion through the Runge-Kutta integration method.

소프트웨어 개발에 있어서 소프트웨어를 시장에 출시하는 계획을 수립하는 것은 소프트웨어를 이루고 있는 기능들을 구현하는 데 제약이 되는 조건들(기술, 자원, 위험, 예산 등)을 만족하면서 계획된 출시기간에 이들 기능들을 할당하는 일이다. 이와 같이 소프트웨어 출시를 계획하는 것은 소프트웨어 제품라인에 대해서 고려할 때 더욱 복잡해진다. 본 연구에서는 소프트웨어 제품라인에 있어서 소프트웨어 출시 계획을 수립하기 위한 문제를 우선순위 제약하의 다수 0-1 배

Software release planning in software development is to assign its features to releases in a specified planning horizon,satisfying technology, resource, risk, and budget constraints. The release planning problembecomes more complicated when the concept of software product lines (SPL) is considered. In this research, a precedence-constrained multiple 0-1 knapsack problem regarding SPL characteristics is formulated to maximize the objective function depending on the value of the release, the importance of stakeholders, the urgency of a feature and its value to stakeholders. As the optimization solution approach, dynamic programming model is developed to solve the precedence-constrained multiple 0-1 knapsack problem as well as a heuristic and reduction algorithm are applied to reduce the size of the problem at each stage