sams
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On page 224 of the 5th edition of Classical Dynamics of Particles and Systems by Stephen T. Thornton and Jerry B. Marion, the authors introduced the ##δ## notation (in section 6.7). This notation is given by Equations (6.88) which are as follows:
$$\delta J = \frac{\partial J}{\partial \alpha}d\alpha$$ $$\delta y = \frac{\partial y}{\partial \alpha}d\alpha$$
I know that the δδ notation stands for the variation from the actual path, but I cannot relate the geometrical interpretation to the above equation. Can anyone please explain the above terms and provide an explanation on why do the right-hand sides of these relations represent the variation (varied path) from the actual path?
Any help is much appreciated. Thank you so much.
$$\delta J = \frac{\partial J}{\partial \alpha}d\alpha$$ $$\delta y = \frac{\partial y}{\partial \alpha}d\alpha$$
I know that the δδ notation stands for the variation from the actual path, but I cannot relate the geometrical interpretation to the above equation. Can anyone please explain the above terms and provide an explanation on why do the right-hand sides of these relations represent the variation (varied path) from the actual path?
Any help is much appreciated. Thank you so much.