Can someone give me the intuition behind not using time as a parameter

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SUMMARY

Using the angle of rotation as a parameter for a Cycloid is preferred over time due to its direct relationship with the physical motion of the wheel. This approach simplifies the mathematical modeling of the Cycloid, allowing for more straightforward calculations of position and velocity. Time, while applicable, introduces unnecessary complexity and can obscure the underlying geometric relationships. Therefore, employing the angle provides clearer insights into the dynamics of the system.

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Can someone give me the intuition behind not using time as a parameter for a Cycloid.
 
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Sorry I mean to say why is using the angle by which the wheel has turned more preferable than using time as a parameter. I understand both can be used.
 


Sorry I mean to say why is using the angle by which the wheel has turned more preferable than using time as a parameter. I understand both can be used.
 

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