Input shaping is an effective open-loop strategy for reducing residual payload oscillation in overhead crane systems, yet its practical performance depends on more than nominal oscillation cancellation. This study develops a coherent analytical treatment of input-function selection, robustness assessment, energy and power interpretation, terminal swing dynamics, input nonuniqueness, double-pendulum modeling, output shaping, and nonzero initial conditions. The main contribution is the integration of these design issues into a consistent set of physical and mathematical criteria for crane-command synthesis. The analysis clarifies the distinction between payload oscillation and structural vibration, explains the limitations of ideal impulse and discontinuous step commands, identifies numerical and analytical issues associated with high-degree polynomial profiles, and highlights exponential and low-order harmonic profiles as tractable smooth alternatives when actuator limits are enforced. Robustness is examined through sensitivity measures over finite parameter intervals rather than by local derivative cancellation alone. Energy arguments show that, for fixed boundary states in an ideal lossless system, total work is determined by the prescribed initial and final states, whereas peak power, root-mean-square power, and actuator effort remain meaningful design objectives. The study further shows that input scaling provides a simple means of adjusting terminal trolley speed after oscillation-suppression conditions are satisfied, and that nearly singular double-pendulum descriptions should be reduced when one pendulum mass is negligible. These findings support implementable input-shaping designs with clearer terminology, stronger physical consistency, and improved relevance to crane operation.