- #1
MikeN232
I need explanation of these formulas for polar coordinate system where position of an object is characterized by 2 vectors: r - from the origin to the object, and Φ - perpendicular to r, in the direction of rotation.
https://drive.google.com/file/d/0ByKDaNybBn_eakJmS3dUVXVZUDA/view?usp=sharing
The 1st one is how we define a vector: product of magnitude by unit vector (which gives a direction), clear;
the 2nd we try to express change in unit vector, which can only change direction = angle of rotation, but why we multiply it then by unit vector Φ, and why ≈ ? Need explanation;
the 3rd we found derivative of position with respect to time;
the 4th, differentiated the 1st formula;
the 5th, substituted 3 into 4;
the 7th, differentiated it for the second time to find acceleration and here we need derivative of unit vector Φ;
8 found derivative of unit vector Φ; how they did it and why unit vector r is here? Need explanation.
9,10 substituted Φ, found acceleration
https://drive.google.com/file/d/0ByKDaNybBn_eakJmS3dUVXVZUDA/view?usp=sharing
The 1st one is how we define a vector: product of magnitude by unit vector (which gives a direction), clear;
the 2nd we try to express change in unit vector, which can only change direction = angle of rotation, but why we multiply it then by unit vector Φ, and why ≈ ? Need explanation;
the 3rd we found derivative of position with respect to time;
the 4th, differentiated the 1st formula;
the 5th, substituted 3 into 4;
the 7th, differentiated it for the second time to find acceleration and here we need derivative of unit vector Φ;
8 found derivative of unit vector Φ; how they did it and why unit vector r is here? Need explanation.
9,10 substituted Φ, found acceleration
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