- #1
Tac-Tics
- 816
- 7
Is there a name for the DE given by Newton's law of gravity:
[tex]f''(x) f(x)^2 = -1[/tex]
?
[tex]f''(x) f(x)^2 = -1[/tex]
?
Tac-Tics said:Is there a name for the DE given by Newton's law of gravity:
[tex]f''(x) f(x)^2 = -1[/tex]
?
I don't know of any specific "name" for it but. since the independent variable, x, does not appear explicitely, it can be solved using "quadrature":Tac-Tics said:Is there a name for the DE given by Newton's law of gravity:
[tex]f''(x) f(x)^2 = -1[/tex]
?
The name for DE (differential equation) given by the law of gravitation is "Newton's second law of motion". It is also known as the "law of universal gravitation".
The law of gravitation states that every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Differential equations are used to describe the motion of objects under the influence of gravitational forces. The law of gravitation is a differential equation because it relates the acceleration of an object to the gravitational force acting on it.
The law of gravitation was discovered by Sir Isaac Newton in 1687. He published it in his famous work "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy).
The law of gravitation governs the motion of objects in our everyday lives. It is responsible for keeping the planets in orbit around the sun, causing objects to fall towards the earth, and even influencing the tides. Without this law, our understanding of the universe and our daily activities would be drastically different.