# Computer Algebra in Applied Mathematics: Introduction to by R.H. Rand

By R.H. Rand

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Extra resources for Computer Algebra in Applied Mathematics: Introduction to Macsyma (Research Notes Inmathematics Series)

Sample text

CII)-(CI6) The boundary conditions are used to find the arbitrary constants KI, K2, K3, K4. ) Plugging the values of the arbitrary constants into the general solution. (CI8) A check. 30 2 Housekeeping in MACSYMA In this chapter we shall discuss some practical questions about how to work with MACSYMA. None of this is really part of computer algebra, but you have to know it to be able to use MACSYMA ~fficiently. The topics which follow are: disk files, special keys, and the editor. Disk Files There are several distinct schemes for saving disk files in MACSYMA, each with its own purpose: 1) To save function definitions or variable values, to be reloaded into a future MACSYMA.

CI8) A check. 30 2 Housekeeping in MACSYMA In this chapter we shall discuss some practical questions about how to work with MACSYMA. None of this is really part of computer algebra, but you have to know it to be able to use MACSYMA ~fficiently. The topics which follow are: disk files, special keys, and the editor. Disk Files There are several distinct schemes for saving disk files in MACSYMA, each with its own purpose: 1) To save function definitions or variable values, to be reloaded into a future MACSYMA.

Note that the chain rule in DERIV now involves partial derivatives with respect to X, Y[O], Y[l], ••. ]. 51 Example 2. Lagrange's Equations with N Degrees of Freedom The motion of a conservative mechanical system with N degrees of freedom is governed by N second order ordinary differential equations which may be written in the form: d ~L 'aL = dt 1q' = 1,2,3, ••• ,N ")q i where L i 0, i = L(q , q' i , t) is called the Lagrangian, and i equals the difference between the kinetic and potential energies of the system.