You have to use the ABAP classes commented above. These ABAP classes allows to work with iCalendar protocol. The only thing I said is that you must keep in mind that an appointment change (reschedule) is done by REQUEST method (vevent).
Check this document by Alexander Mintchev about calendar appointments. There, you can see what I am talking about. You must understand iCalendar protocol first before managing appointments with ABAP API (CL_APPOINTMENT).