In the context of classical mechanics, is it possible to have an isolated system which does not lose/gain particles, but whose mass changes over time? I have been trying to think of such an example for a while, but have been unable to come up with one.

I understand that this phenomenon is common in special relativity, but, as I have been told, Newton did not postulate mass invariance for classical mechanics either. The question is also somewhat related to Newton's formulation of the second principle,

$$\overrightarrow{F}=\frac{\overrightarrow{dp}}{dt}$$

which, given that the system referred to does not lose/gain particles, could also be written as

$$\overrightarrow{F}=m\frac{\overrightarrow{dv}}{dt} + \frac{dm}{dt}\overrightarrow{v}$$

However, I have never seen an example outside of relativity where this formula is used. Is there any such example in classical mechanics?

In the context of Newtonian mechanics, is it possible to have an isolated system which does not lose/gain particles, but whose mass changes over time? I have been trying to think of such an example for a while, but have been unable to come up with one.

I understand that this phenomenon is common in special relativity, but, as I have been told, Newton did not postulate mass invariance for Newtonian mechanics either. The question is also somewhat related to Newton's formulation of the second principle,

$$\overrightarrow{F}=\frac{\overrightarrow{dp}}{dt}$$

which, given that the system referred to does not lose/gain particles, could also be written as

$$\overrightarrow{F}=m\frac{\overrightarrow{dv}}{dt} + \frac{dm}{dt}\overrightarrow{v}$$

However, I have never seen an example outside of relativity where this formula is used. Is there any such example in Newtonian mechanics?