Principle of Conservation of Energy

Physical Law

Let $B$ be a body in a force field.

Let $B$ be subject only to forces within that force field.

Let $P$ be the potential energy of $B$.

Let $K$ be the kinetic energy of $B$.

Then:

$P + K = \text{constant}$

Historical Note

The first correct statement of the Principle of Conservation of Energy was made by Christiaan Huygens in a presentation to the Royal Society of London in $1669$.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 5$: Falling Bodies and Other Rate Problems
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): conservative force
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): energy
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): kinetic energy
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): potential energy
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conservative force
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): energy
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kinetic energy
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): potential energy