Is the earth in a non-inertial reference frame?

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The Earth exhibits a uniform tangential velocity but is considered a non-inertial reference frame due to its rotation. The centripetal acceleration resulting from this rotation contributes to its non-inertial status. In Newtonian physics, gravity is viewed as a real force causing proper acceleration, which categorizes orbiting bodies as non-inertial. Conversely, in general relativity, free-falling objects are considered inertial, but inertial frames are only locally valid at the planet's center, making the surface non-inertial. Therefore, the Earth is classified as a non-inertial frame due to its rotational dynamics and gravitational influences.
deadscientist
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So I would agree that it has a uniform tangential velocity but would the centripetal acceleration of the Earth put it in a non inertial frame.
 
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The rest frame of the Earth is noninertial due to rotaion around its own axis. As for the centripetal accelleration due to suns gravity, it depends which theory of gravity you use:

In Newtons model gravity is a real force that causes proper acceleration, which makes orbiting bodies noninertial (even nonrotationg ones).

In general relativity free falling objects are inertial, but inertial frames exist only locally, at the center of the planet. The surface is very noninertial.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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