joh

Manage to find what b1, b2 and b3 are. Thanks a lot for all your tips.

I probably didn't present the problem very well. I did not expand the equation. This is done in a paper. The issue is that the paper does not explain how this happened nor can I think of a way to achieve this (the main problem is that I can't figure out were the partial came from, I did consider using a taylor expansion but got nowhere). In the paper the following information is available: http://s20.postimg.org/3mqwmdgf1/image.png Equations (1) and (2) are the force balance on the glass surface shown in the third picture. After these two equations are expanded in equation (3) and (4) they are inserted in the equation of motion of the system. P = force (as shown in figures) angles as shown in figures [latex]\mu_0[/latex] = friction coefficient v = relative velocity between the lip and glass [latex]\frac{\partial \mu}{\partial v}[/latex]: behavior is described by the stribeck curve I need to now how the expansion takes place in order to know what b1, b2 and b3 are. P.S.: Apologies for the consistency issues in the first post

An equation of the following form is given: [latex]c=-a_1*\sin(\alpha)+a_2*\cos(\alpha)[/latex] next by expanding the equation above the following equation is obtained: [latex]c=-b_1*\sin(\beta-\delta)\gamma-b_2(\frac{\partial u}{\partial v})\dot \gamma[/latex] i have rewritten the first equation to: [latex]c=\sqrt{c_1^2+c_1^2}\cos(\alpha-\epsilon)=\sqrt{(c_1^2+c_2^2)(1-\sin^2(\alpha-\epsilon))}[/latex] where [latex]\epsilon=\tan^{-1}(c_2/c_1)[/latex] However, I don't think this is the correct path to obtaining the expanded equation and if it is I can't see what the next step should be. How do they obtain the expanded equation?