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Recent research has looked to supplement or even replace the batteries in embedded computing systems with energy harvesting, where energy is derived from the device's environment. However, such supplies are generally unpredictable and highly variable, and hence systems typically incorporate large external energy buffers (e.g., supercapacitors) to sustain computation; however, these pose environmental issues and increase system size and cost. This article proposes Momentum, a general power-neutral methodology, with intrinsic system-wide maximum power point tracking, that can be applied to a wide range of different computing systems, where the system dynamically scales its performance (and hence power consumption) to optimize computational progress depending on the power availability. Momentum enables the system to operate around an efficient operating voltage, maximizing forward application execution, without adding any external tracking or control units. This methodology combines at runtime (1) a hierarchical control strategy that utilizes available power management controls (such as dynamic voltage and frequency scaling, and core hot-plugging) to achieve efficient power-neutral operation; (2) a software-based maximum power point tracking scheme (unlike existing approaches, this does not require any additional hardware), which adapts the system power consumption so that it can work at the optimal operating voltage, considering the efficiency of the entire system rather than just the energy harvester; and (3) experimental validation on two different scales of computing system: a low power microcontroller (operating from the already-present 4.7µF decoupling capacitance) and a multi-processor system-on-chip (operating from 15.4mF added capacitance). Experimental results from both a controlled supply and energy harvesting source show that Momentum operates correctly on both platforms and exhibits improvements in forward application execution of up to 11% when compared to existing power-neutral approaches and 46% compared to existing static approaches. [ABSTRACT FROM AUTHOR]