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I am simulating a random walk on a sphere with unit radius. I want to move from current location p_t to the new location p_{t+1} along the big circle, whose arc has an angle omega relative to p_t's latitude. I tried using the law of cosine. But at the poles, the law of cosine diverges. Can anyone help find a method that works for all location on the sphere? Thanks!

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# How to simulate a random walk on a sphere

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