Hierarchical Federated Learning (HFL) alleviates the trade-off between communication overhead and privacy protection in mobile scenarios via multi-level aggregation and mobility consideration. However, its idealized convex loss assumption and full-dimension parameter upload deviate from real-world non-convex tasks and edge channel constraints, causing excessive energy consumption, high communication cost, and compromised convergence that hinder practical deployment. To address these issues in mobile/UAV networks, this paper proposes an energy-efficient optimization scheme for HFL under non-convex loss, integrating a dynamically adjustable partial-dimension model upload mechanism. By screening key update dimensions, the scheme reduces uploaded data volume. We construct a total energy minimization model that incorporates communication/computation energy formulas related to upload dimensions and introduces an attendance rate constraint to guarantee learning performance. Using Lyapunov optimization, the long-term optimization problem is transformed into single-round solvable subproblems, with a step-by-step strategy balancing minimal energy consumption and model accuracy. Simulation results show that compared with the original HFL algorithm, our proposed scheme achieves significant energy reduction while maintaining high test accuracy, verifying the positive impact of mobility on system performance.