Someone has indeed taxed my brain. And this is a challenging question which needs considerable thought to answer. The difference between equilibrium, equanimity and equipoise .
The person has presciently pointed out that there is a subtle difference and requires immense skill, craft and dexterity to nuance the meaning or import of the words.
Equilibrium implies that an individual has accepted that life is all about opposites, at all times; joy and misery, jealousy and contentment or anger and calmness. To expect that only one or the other would prevail is incorrect.
Equanimity is the real-time application of the state of equilibrium, that is to accept with grace and without rancour all the highs and lows, knowing that ‘this too shall pass’.
Equipoise would imply the ability to quickly restore oneself to a state of equanimity whenever equilibrium is disturbed
To my mind, our ancient Rishi/ Munis and sages were in that state through vigorous Tapas.
Evolved souls like sage Patanjali, Gautama Buddha , Adi Shankaracharya and in the present generation Guruji are in a constant state of the three E's - Equilibrium, Equipoise and Equanimity. Such individuals remain unruffled irrespective of the situation.
One E or two of the Es are always missing among ordinary mortals, seekers , savants traversing the path to attain the three E's.
Second let us take the case of the unique rhythmic breathing technique of Sudarshan Kriya. Through the three cycles Guruji take us to the elevated state of equilibrium, equipoise and equanimity. In such a state we cannot distinguish between the three E's and suffused with pristine love to almighty God, our creator and are purged of anger and all antipathetic thoughts.
Today , on completion of the three day course - Happiness Programme( or Prana) for recovering alcoholics and drug addicts at the rehabilitation centre , I am brimful of equanimity, equipoise and equilibrium. Infact after the intro talk , I fell sick and was feeling highly at unease as I could not take the course. Upon completion of the course and seeing the shining faces and demeanor of the addicts , I felt at peace.
Therefore as H. H. Sri Sri Ravi Shankar aptly says that taking up responsibility empowers you and we reach a true sense of contentment.
Thus contentment / compassion and enlightenment = equilibrium, equanimity and equipoise.
I am sure , the individual who has triggered my mind by asking the difference between equanimity, equipoise and equilibrium would have been in this state of jollity and sheer ecstasy after conducting various Advanced Meditation Courses , writing, sharing the knowledge of Yoga Vashista and singing in Satsangs especially during Navaratri festival.
In the ultimate analysis equilibrium, equanimity and equipoise are emotions of the triad called Happiness. But this can be attained only without the feeling of doership. As the 4th E- Ego will trample , our state of mind.