Does mechanical energy means total energy?

Question

I know that mechanical energy is the sum of kinetic energy and potential energy. But there is a sentence in the book like this:

'Our primary goal, however, is to find the energies associated with these states. We know that the total energy of a system is equal to the kinetic energy plus the potential energy.'

However, as far as I know, this is mechanical energy. Is total energy the same as mechanical energy?

Answer 1

The total energy is the same as the sum of the kinetic and potential energies. However, the energy function, i.e. Jacobi's integral is not always the same as the total energy. Jacobi's integral or the energy function is more representative of the mechanical energy and is given by: $$h(q_1,\ldots,q_n; \dot q_1\ldots, \dot q_n; t)=\sum_j\dot q_j{\partial L\over\partial \dot q_j}-L.$$ The two coincide whenever the forces are derivable from a potential function of the gernalized coordinates only, and the kinetic energy is a homogeneous quadratic function in the generalized velocities (cf. Goldstein. $3^{rd}$ed., 62-63). For example, when one has velocity dependent potential as in electromagnetism, then one will not have the mechanical energy equal to the total energy.

Answer 2

"total energy of a system is equal to the kinetic energy plus the potential energy.'" only holds in mechanic so of cause you have other energies, So it should say total mechanical energy of a system is equal to the kinetic energy plus the potential energy.