This paper deals with real-time scheduling of homogeneous multi-core platforms powered by a battery to be periodically recharged. A system is composed of reconfigurable real-time dependent and periodic tasks to be assigned to different cores interconnected by a network-on-chip (NoC). The system is subject to reconfigurations, which are automatic operations allowing the addition and/or removal of tasks as well as their exchanged messages on the NoC. Consequently, any reconfigu-ration can violate real-time and energy constraints on cores as well as the NoC when the energy is unavailable until the next recharge. A novel periodic task model based on elastic coefficients and a new scheduling strategy are proposed to compute useful temporal parameters allowing for tasks and messages to meet the related constraints while controlling the communication cost on the NoC. This strategy is compared with an ILP-based optimal solution, and a tool named OptimalMappingTasks is developed to run different simulations that prove the originality of the paper's contribution.