I am not able to solve value of 3 constants with three equations

Question

Sahir Jan 2021-11-3

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https://ww2.mathworks.cn/matlabcentral/answers/1578225-i-am-not-able-to-solve-value-of-3-constants-with-three-equations

回答： Bjorn Gustavsson 2021-11-3

c1*(cos(b*d)+cosh(b*d))+c3*(sin(b*d)+sinh(b*d))+c4*(sin(b*d)-sinh(b*d))=0

c1*(cos(b*(L-d))+cosh(b*(L-d)))+c3*(sin(b*(L-d))+sinh(b*(L-d)))+c4*(sin(b*(L-d))-sinh(b*(L-d)))=0

c1*(-cos(b*L)+cosh(b*L))+c3*(-sin(b*L)+sinh(b*L))+c4*(-sin(b*L)-sinh(b*L))=0

I have the following three equations and have to find the value for c1, c3 and c4. Can someone help me with the code

Thank you

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Answer 1

Bjorn Gustavsson 2021-11-3

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For given values of b, d, and L you have a standard system of linear equation. An obvious solution to these equations are all ci = 0. Each equation will be an equation for a plane in the three-dimensional space for c1, c2, c4. From there you can use geometric arguments that either 2 planes are parallel and doesn't intersect or intersects along a line, in the second case such a line either intersects the third plane, lies in the third plane or does not intersect the plane, the third case is out since we know that [0 0 0] is a solution, therefor either [0 0 0] is the only solution or lies on the line. What you'll have to do is to check whether there is a line of solutions or the one and only solution.

HTH