For constant symmetric mass and stiffness matrices, satisfies . Every equation with antisymmetric conserves this same mechanical energy, because . Thus a scalar conservation law alone cannot select the dynamics of several degrees of freedom. The specified conservative-force or Lagrangian structure supplies the missing information.
The accounting of energy entering, leaving and being stored in a system. A global climate energy budget distinguishes top-of-atmosphere radiative imbalance from internal ocean–surface heat exchange.
An energy balance accounts for the change of stored energy as inputs minus outputs. For mechanical motion, externally supplied power and dissipative losses must be included before imposing a conserved mechanical energy.

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Conservation of energy by Wikipedia Bot 1
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The conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed in an isolated system; it can only change forms. This means that the total energy of an isolated system remains constant over time, though it may transform from one type of energy to another, such as from kinetic energy (the energy of motion) to potential energy (stored energy based on position) or thermal energy (heat).
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Conservation of energy by Ciro Santilli 40 Updated 2025-07-16
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