One of the earliest and best descriptions is by a published paper of the person it's credited to: J. K. Clapp, "An inductance-capacitance oscillator of unusual frequency stability", Proc. IRE, vol. 367, pp. 356-358, Mar. 1948. I couldn't find a link for it though.
In an oscillator with a stabilised amplitude, there's often a switch of some kind involved with the amplitude stabilising. Many years ago I did a precision low frequency oscillator, with bandgap-reference precision amplitude stability. It was based on a Wein oscillator, with a variable-gain element controlled by DC voltage. The amplitude peak level was detected by a 'class-c' switch, which fed narrow 'wave-tip' pulses into a leaky charge pump, then into the variable gain element to close the amplitude control loop. It was very simple, only one opamp, a bandgap reg and 3 transistors.
Another variation of stabilised amplitude oscillator is the 'thermistor regulated' oscillator. The amplitude of the oscillator is regulated by the self heating of a thermistor in response to amplitude. (I tried this oscillator previously before I developed the bandgap-stabiliised circuit better and cheaper in the company's product)
The J-FET circuit in this thread is somewhere in between these types. It's a bandpass tuned amplifier, with positive feedback. The gain of this amplifier is variable, according to a shaped curve: gate voltage/drain current. Generally, the more negative the gate voltage, the less gain the FET has. When the oscillator has stabilised, the LC tank resembles a clock pendulum, and the j-fet the escapement. There is a start up, that I'd described in an earlier posting.
Like the bandgap-stabilised oscillator I described above, the j-fet conducts drain current only when the postive sinusoid biases the j-fet on. In practice, in a well-designed circuit, it will only conduct on the positive tips of the RF wave. Since this conduction period is considerably less than 50 % is why it's called a "class c oscillator".
The start up is described* in:
https://www.electro-tech-online.com/custompdfs/2009/07/322Lecture24-1.pdf apologies for the link sometimes not working, if it doesn't at the time you try it, try again later.
*Thanks go to Keith W. Whites, Professor of Department of Electrical and Computer Engineering, The South Dakota School of Technology, Rapid City
**broken link removed**